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Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

Jürgen Jost (Autor)

Buch | Softcover

XVIII, 282 Seiten

2006 | 3. Third Edition 2006
Springer Berlin (Verlag)
978-3-540-33065-3 (ISBN)

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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.

Topological Foundations.- Differential Geometry of Riemann Surfaces.- Harmonic Maps.- Teichmüller Spaces.- Geometric Structures on Riemann Surfaces.- Erratum to: Characterizing Programming Systems Allowing Program Self-reference.

From the reviews:

"Compact Riemann Surfaces: An Introduction to Contemporary Mathematics starts off with a wonderful Preface containing a good deal of history, as well as Jost's explicit dictum that there are three foci around which the whole subject revolves ... . Jost's presentation is quite accessible, modulo a lot of diligence on the part of the reader. It's a very good and useful book, very well-written and thorough." (Michael Berg, MathDL, April, 2007)

From the reviews of the third edition:

"Geometrical facts about Riemann surfaces are as 'nice' as possible, and they often provide the intuition and motivation for generalizations to other curves, manifolds or varieties. The Riemann-Roch theorem ... is a prime example of this influence. This book is amazing, very well written, accessible and works as a first course on Riemannian Surfaces I recommend to the all readers interested in Geometry and Riemannian Geometry." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)

From the reviews:"Compact Riemann Surfaces: An Introduction to Contemporary Mathematics starts off with a wonderful Preface containing a good deal of history, as well as Jost’s explicit dictum that there are three foci around which the whole subject revolves … . Jost’s presentation is quite accessible, modulo a lot of diligence on the part of the reader. It’s a very good and useful book, very well-written and thorough." (Michael Berg, MathDL, April, 2007)From the reviews of the third edition:“Geometrical facts about Riemann surfaces are as ‘nice’ as possible, and they often provide the intuition and motivation for generalizations to other curves, manifolds or varieties. The Riemann–Roch theorem … is a prime example of this influence. This book is amazing, very well written, accessible and works as a first course on Riemannian Surfaces I recommend to the all readers interested in Geometry and Riemannian Geometry.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)

Erscheint lt. Verlag	19.6.2006
Reihe/Serie	Universitext
Zusatzinfo	XVIII, 282 p. 23 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	476 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Differential Geometry • Hardcover, Softcover / Mathematik/Geometrie • harmonic maps • HC/Mathematik/Analysis • HC/Mathematik/Geometrie • Hyberbolic geometry • Hyperbolic Geometry • Riemann-Roch theorem • Riemannsche Flächen • Riemann Surfaces • Teichmüller theory
ISBN-10	3-540-33065-8 / 3540330658
ISBN-13	978-3-540-33065-3 / 9783540330653
Zustand	Neuware