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The Geometry of Total Curvature on Complete Open Surfaces : Cambridge Tracts in Mathematics - Katsuhiro Shiohama

The Geometry of Total Curvature on Complete Open Surfaces

Cambridge Tracts in Mathematics


Published: 22nd December 2003
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This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

'...carefully written ... a very valuable addition to libraries.' Zentralblatt MATH

Riemannian geometry
Classical results by Cohn-Vossen and Huber
The ideal boundary
The cut loci of complete open surfaces
Isoperimetric inequalities
Mass of rays
Poles and cut loci of a surface of revolution
Behaviour of geodesics
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521450546
ISBN-10: 0521450543
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 294
Published: 22nd December 2003
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.6 x 16.1  x 2.1
Weight (kg): 0.54