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Compact Riemann Surfaces: An Introduction to Contemporary Mathematics (Universitext) - Softcover

Jost, Jürgen

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9783540432999: Compact Riemann Surfaces: An Introduction to Contemporary Mathematics (Universitext)
Softcover
ISBN 10: 354043299X ISBN 13: 9783540432999
Publisher: Springer, 2002

Synopsis

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 2nd edition the author has further improved aspects of presentation of various parts of the text.

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Language Notes

Text: English (translation)
Original Language: German

Review

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)

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2002
Language
English
ISBN 10 
354043299X
ISBN 13 
9783540432999
Binding
Paperback
Edition number
2
Number of pages
281
Rating
  • 4.00 out of 5 stars
    5 ratings by Goodreads