Metric Spaces Convexity and Nonpositive Curvature 2nd Edition by Athanase Papadopoulos ISBN 3037190108 9783037190104

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Product details: 

ISBN 10: 3037190108

ISBN 13: 9783037190104

Author: Athanase Papadopoulos
Metric Spaces, Convexity and Nonpositive Curvature (2nd Revised Edition) offers a systematic and rigorous introduction to metric geometry, focusing on spaces of nonpositive curvature in the sense of Busemann—where the distance function obeys a convexity condition. The book develops foundational concepts such as geodesics, convexity, and functions within metric spaces, and illustrates these ideas with examples drawn from hyperbolic geometry, Hilbert geometry, and Teichmüller theory. This revised edition includes corrections, new additions, updated bibliography, and enhanced presentation of the theory, making it a valuable resource for graduate students and researchers in geometry, topology, and analysis. 

Table of contents: 

1. Lengths of Paths in Metric Spaces

2. Length Spaces and Geodesic Spaces

3. Maps Between Metric Spaces

4. Distances

5. Convexity in Vector Spaces

6. Convex Functions

7. Strictly Convex Normed Vector Spaces

8. Busemann Spaces

9. Locally Convex Spaces

10. Asymptotic Rays and the Visual Boundary

11. Isometries

12. Busemann Functions, Corays, and Horospheres

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Tags: Athanase Papadopoulos, Metric Spaces, Convexity and Nonpositive