Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective: the text systematically explores the connection with other fields of mathematics. The book 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. Compact Riemann Surfaces is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Klappentext

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book 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. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Inhalt

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