Metric Spaces, Convexity and Nonpositive Curvature

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More About This Textbook

Overview

"This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. The book also contains a systematic introduction to the theory of geodesics in metric spaces, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature." "The concepts and the techniques are illustrated by many examples from classical hyperbolic geometry and from the theory of Teichmuller spaces." The book is useful for students and researchers in geometry, topology and analysis.
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Product Details

  • ISBN-13: 9783037190104
  • Publisher: American Mathematical Society
  • Publication date: 12/31/2004
  • Series: Irma Lectures in Mathematics and Theoret
  • Edition description: New Edition
  • Pages: 300
  • Product dimensions: 6.70 (w) x 9.50 (h) x 0.60 (d)

Table of Contents

Introduction : some historical markers 1
1 Lengths of paths in metric spaces 10
2 Length spaces and geodesic spaces 34
3 Maps between metric spaces 79
4 Distances 103
5 Convexity in vector spaces 127
6 Convex functions 159
7 Strictly convex normed vector spaces 178
8 Busemann spaces 187
9 Locally convex spaces 210
10 Asymptotic rays and the visual boundary 229
11 Isometries 241
12 Busemann functions, co-rays and horospheres 261
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