Riemann Surfaces
by Beardon, AlanEdition: 2nd
Format: Hardcover
Pub. Date: 2016-08-31
Publisher(s): Cambridge Univ Pr
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Summary
This textbook, aimed at advanced undergraduate or beginning graduate students in mathematics, introduces both the theory of Riemann surfaces, and of analytic functions between Riemann surfaces. The first half of the book describes the basic theory, the second half develops the theory of harmonic and subharmonic functions on a Riemann surface, and culminates with a detailed proof of the famous Uniformisation Theorem and some of its applications to Riemann surface theory. The book is a major revision of the author's earlier 'Primer', with new chapters and more exercises and examples.
Table of Contents
| 1. Complex analysis | |
| 2. Basic topology | |
| 3. Riemann surfaces | |
| 4. Examples | |
| 5. Analytic functions | |
| 6. Existence of analytic funtions | |
| 7. Analytic continuation | |
| 8. Covering spaces | |
| 9. Harmonic functions | |
| 10. Additional topics. |
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