Metric Spaces, Convexity and Nonpositive Curvature
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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Some historical markers
Lengths of paths in metric spaces
Length spaces and geodesic spaces
Maps between metric spaces
Convexity in vector spaces
Strictly convex normed vector spaces
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