Geometry of Total Curvature on Complete Open Surfaces~tqw~ darksiderg

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Geometry of Total Curvature on Complete Open Surfaces
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Release NotesThis independent account of modern ideas in differential geometry shows how they
can be used to understand and extend classical results in integral geometry. The
authors explore the influence of total curvature on the metric structure of
complete, non-compact Riemannian 2-manifolds, although their work can be
extended to more general spaces. Each chapter features open problems, making the
volume a suitable learning aid for graduate students and non-specialists who
seek an introduction to this modern area of differential geometry.

Table of Contents

Preface
1 Riemannian geometry 1
2 The classical results of Cohn-Vossen and Huber 41
3 The ideal boundary 75
4 The cut loci of complete open surfaces 133
5 Isoperimetric inequalities 165
6 Mass of rays 187
7 The poles and cut loci of a surface of revolution 207
8 The behavior of geodesics 243
References 275
Index 281

Product Details

* ISBN: 0521450543
* ISBN-13: 9780521450546
* Format: Hardcover, 294pp
* Publisher: Cambridge University Press
* Pub. Date: November 2003
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