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Introduction and overview |
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1 | (31) |
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4 | (9) |
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n-Dimensional quasiconformal mappings |
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13 | (3) |
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16 | (1) |
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17 | (1) |
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Stability and rigidity phenomena |
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18 | (1) |
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Quasiconformal structures on manifolds |
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19 | (4) |
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23 | (2) |
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Non-linear potential theory |
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25 | (1) |
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Singular integral operators |
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25 | (2) |
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27 | (1) |
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Quasiconformal groups, semigroups and dynamics |
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27 | (2) |
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Continuum mechanics and non-linear elasticity |
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29 | (2) |
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31 | (1) |
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32 | (11) |
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The Cauchy-Riemann system |
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32 | (2) |
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34 | (2) |
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The Liouville theorem (smooth case) |
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36 | (1) |
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36 | (3) |
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39 | (1) |
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40 | (1) |
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41 | (2) |
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Stability of the Mobius group |
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43 | (10) |
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43 | (2) |
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45 | (2) |
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47 | (1) |
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Passing Harnack inequalities on to Mt |
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48 | (2) |
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50 | (3) |
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Sobolev theory and function spaces |
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53 | (32) |
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53 | (4) |
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Definitions of Sobolev spaces |
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57 | (1) |
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57 | (1) |
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58 | (1) |
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Pointwise coincidence of Sobolev functions |
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59 | (1) |
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Alternative characterizations |
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60 | (3) |
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Cross product of gradient fields |
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63 | (2) |
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65 | (2) |
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Subharmonic distributions |
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67 | (1) |
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68 | (5) |
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Duals and compact embeddings |
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73 | (1) |
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74 | (6) |
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80 | (5) |
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85 | (14) |
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85 | (2) |
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87 | (3) |
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90 | (3) |
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93 | (2) |
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Continuity of the Jacobian |
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95 | (2) |
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A formula for the Jacobian |
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97 | (1) |
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98 | (1) |
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Mapping of finite distortion |
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99 | (39) |
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100 | (4) |
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Integrability of the Jacobian |
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104 | (1) |
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105 | (3) |
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108 | (4) |
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112 | (26) |
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112 | (3) |
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115 | (3) |
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118 | (1) |
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The Zorich exponential map |
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119 | (3) |
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122 | (4) |
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Squeezing the Sierpinski sponge |
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126 | (8) |
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134 | (4) |
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138 | (31) |
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140 | (3) |
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The L1 integrability of the Jacobian |
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143 | (5) |
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Weakly monotone functions |
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148 | (2) |
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150 | (2) |
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152 | (4) |
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Exponentially integrable outer distortion |
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156 | (4) |
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160 | (3) |
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Fundamental LP-inequality for the Jacobian |
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163 | (6) |
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A class of Orlicz functions |
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164 | (2) |
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Another proof of Corollary 7.2.1 |
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166 | (3) |
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169 | (39) |
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Distributional Jacobians revisited |
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169 | (3) |
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Weak convergence of Jacobians |
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172 | (3) |
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175 | (1) |
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Improving the degree of integrability |
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176 | (5) |
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Weak limits and orientation |
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181 | (4) |
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185 | (1) |
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186 | (1) |
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187 | (4) |
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188 | (2) |
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Polyconvexity of distortion functions |
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190 | (1) |
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191 | (2) |
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Lower semicontinuity of the distortion |
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193 | (4) |
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The failure of lower semicontinuity |
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197 | (3) |
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200 | (1) |
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Local injectivity revisited |
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201 | (4) |
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Compactness for exponentially integrable distortion |
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205 | (3) |
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Topics from Multilinear Algebra |
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208 | (14) |
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208 | (1) |
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209 | (2) |
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211 | (1) |
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211 | (1) |
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212 | (1) |
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213 | (3) |
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216 | (1) |
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217 | (3) |
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Hadamard-Schwarz inequality |
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220 | (1) |
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Submultiplicity of the distortion |
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221 | (1) |
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222 | (18) |
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222 | (6) |
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Pullback of differential forms |
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228 | (1) |
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229 | (3) |
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Orlicz-Sobolev spaces of differential forms |
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232 | (2) |
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234 | (2) |
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The Hodge decomposition in Rn |
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236 | (4) |
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240 | (63) |
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240 | (4) |
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244 | (6) |
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245 | (5) |
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250 | (1) |
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251 | (2) |
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253 | (2) |
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255 | (2) |
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Solutions for integrable distortion |
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257 | (2) |
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Distortion in the exponential class |
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259 | (5) |
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261 | (1) |
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262 | (2) |
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Distortion in the subexponential class |
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264 | (4) |
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264 | (1) |
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265 | (2) |
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267 | (1) |
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268 | (16) |
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Results from harmonic analysis |
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269 | (1) |
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Existence for exponentially integrable distortion |
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270 | (6) |
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276 | (2) |
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278 | (2) |
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Existence for subexponentially integrable distortion |
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280 | (4) |
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284 | (5) |
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289 | (3) |
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Examples and non-uniqueness |
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292 | (7) |
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299 | (1) |
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300 | (1) |
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301 | (2) |
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303 | (34) |
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Singular integral operators |
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303 | (5) |
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308 | (4) |
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Trivial extension of a scalar operator |
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312 | (1) |
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313 | (2) |
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The real method of rotation |
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315 | (1) |
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The complex method of rotation |
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316 | (3) |
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319 | (2) |
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The tensor product of Riesz transforms |
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321 | (2) |
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Dirac operators and the Hilbert transform on forms |
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323 | (7) |
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The Lp-norms of the Hilbert transform on forms |
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330 | (2) |
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332 | (1) |
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333 | (4) |
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337 | (17) |
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337 | (3) |
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The complex method of interpolation |
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340 | (3) |
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Jacobians and wedge products revisited |
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343 | (2) |
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The H1-theory of wedge products |
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345 | (2) |
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347 | (3) |
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Estimates beyond the natural exponent |
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350 | (2) |
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Proof of the fundamental inequality for Jacobians |
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352 | (2) |
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354 | (16) |
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356 | (1) |
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Calderon-Zygmund decomposition |
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357 | (2) |
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Gehring's lemma in Orlicz spaces |
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359 | (4) |
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363 | (4) |
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367 | (3) |
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370 | (31) |
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370 | (5) |
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Absolute minima of variational integrals |
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375 | (5) |
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380 | (6) |
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Equations at the level of exterior algebra |
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386 | (5) |
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391 | (2) |
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393 | (5) |
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398 | (3) |
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Topological properties of mappings of bounded distortion |
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401 | (30) |
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402 | (3) |
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405 | (1) |
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406 | (4) |
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410 | (1) |
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410 | (1) |
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411 | (3) |
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Sets of zero conformal capacity |
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414 | (2) |
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Qualitative analysis near polar points |
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416 | (3) |
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Local injectivity of smooth mappings |
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419 | (3) |
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The Jacobian is non-vanishing |
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422 | (1) |
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423 | (3) |
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Openness and discreteness for mappings of bounded distortion |
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426 | (1) |
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427 | (1) |
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428 | (3) |
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Painleve's theorem in space |
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431 | (9) |
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Painleve's theorem in the plane |
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431 | (1) |
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Hausdorff dimension and capacity |
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432 | (2) |
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Removability of singularities |
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434 | (3) |
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437 | (3) |
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440 | (27) |
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441 | (2) |
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Integrability theorems in even dimensions |
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443 | (3) |
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Mappings with exponentially integrable distortion |
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446 | (3) |
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449 | (3) |
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452 | (8) |
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460 | (1) |
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461 | (6) |
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Picard and Montel theorems in space |
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467 | (19) |
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Picard's theorem in space |
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468 | (1) |
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Serrin's theorem and Harnack functions |
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468 | (1) |
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Estimates in H⊖ (Rn) |
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469 | (3) |
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Harnack inequalities near zeros |
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472 | (3) |
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Collections of Harnack functions |
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475 | (2) |
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Proof of Rickman's theorem |
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477 | (3) |
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480 | (3) |
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Montel's theorem in space |
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483 | (1) |
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484 | (2) |
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486 | (7) |
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486 | (3) |
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489 | (2) |
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491 | (2) |
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Uniformly quasiregular mappings |
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493 | (17) |
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A first uniqueness result |
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494 | (2) |
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496 | (3) |
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499 | (2) |
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501 | (4) |
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Invariant conformal structures |
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505 | (5) |
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510 | (18) |
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511 | (2) |
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The elementary quasiconformal groups |
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513 | (4) |
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Non-elementary quasiconformal groups |
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517 | (2) |
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519 | (1) |
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520 | (4) |
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524 | (3) |
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527 | (1) |
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Analytic continuation for Beltrami Systems |
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528 | (3) |
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528 | (1) |
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529 | (1) |
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530 | (1) |
Bibliography |
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531 | (16) |
Index |
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547 | |