Compact Riemann Surfaces: An Introduction to Contemporary Mathematics

Description

Publisher: Springer
Language: English
ISBN: 3540330658
Paperback: 282 pages
Data: Aug 2006
Format: PDF
Description: Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichm¨¹ller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

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