Compact Riemann Surfaces: An Introduction to Contemporary Mathematics

Jürgen Jost

Springer Berlin Heidelberg, Jun 19, 2006 - Mathematics - 282 pages

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 Teichmüller 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.

About the author

Jurgen Jost is Codirector of the Max Plank Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA.

Bibliographic information

• Title: Compact Riemann Surfaces: An Introduction to Contemporary Mathematics
• Author: Jürgen Jost
• Edition: 3, illustrated
• Publisher: Springer Berlin Heidelberg, 2006
• ISBN: 3540330658, 9783540330653
• Length: 282 pages
• Subjects: Mathematics / Geometry / Differential; Mathematics / Geometry / General