Author	Jost, Jรผrgen. author
Title	Compact Riemann Surfaces [electronic resource] : An Introduction to Contemporary Mathematics / by Jรผrgen Jost
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997
Connect to	http://dx.doi.org/10.1007/978-3-662-03446-0
Descript	XIV, 295 p. online resource

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 Teichmรผller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps

1. Topological Foundations -- 2. Differential Geometry of Riemann Surfaces -- 3. Harmonic Maps -- 4. Teichmรผller Spaces -- 5. Geometric Structures on Riemann Surfaces -- Sources and References -- Index of Notation

1. Mathematics
2. Differential geometry
3. Mathematics
4. Differential Geometry