Global Riemannian Geometry
by Markvorsen, Steen; Min-Oo, MaungFormat: Paperback
Pub. Date: 2003-08-01
Publisher(s): Birkhauser
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Summary
The book contains a clear exposition of two contemporary topics in modern differential geometry:- distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature- the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold.It is intended for both graduate students and researchers who want to get a quick and modern introduction to these topics.
Table of Contents
| Distance Geometric Analysis on Manifolds | |
| Appetizer and Introduction | p. 1 |
| The Comparison Setting and Preliminaries | p. 1 |
| Analysis of Restricted Distance Functions | p. 2 |
| Concerning the Setting and Notation | p. 8 |
| Green's Formulae and the Co-area Formula | p. 12 |
| The First Dirichlet Eigenvalue Comparison Theorem | p. 13 |
| Isoperimetric Relations | p. 18 |
| Mean Exit Time Comparison | p. 25 |
| Capacity Comparison | p. 27 |
| The Kelvin-Nevanlinna-Royden Criteria for Transience | p. 31 |
| Surfaces of Revolution | p. 34 |
| Warped Products | p. 37 |
| Answering the Questions in the Appetizer | p. 39 |
| A Sufficient Condition for Hyperbolicity | p. 41 |
| Graphs and Flows | p. 44 |
| Scherk's Graph is Transient | p. 46 |
| The Dirac Operator in Geometry and Physics | |
| Spinors and the Dirac Operator | p. 56 |
| Gromov's K-Area | p. 64 |
| Positive Mass Theorems | p. 76 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
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