# Metric Spaces, Convexity and Nonpositive Curvature: Second Edition

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*Athanase Papadopoulos*

A publication of the European Mathematical Society

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
metric geometry, 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, in
particular from hyperbolic geometry, Hilbert geometry and Teichmüller
theory.

For the second edition, some corrections and a few additions have been
made, and the bibliography has been updated.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in geometry, topology, and analysis.