Metric Spaces, Convexity and Nonpositive Curvature (IRMA Lectures in Mathematics and Theoretical Physics)

This book covers metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. Also contained is a systematic introduction to the theory of geodesics as well as a detailed presentation of some facets of convexity theory, which are useful in the study of nonpositive curvature. Concepts and techniques discussed in the volume are illustrated by many examples from classical hyperbolic geometry and from the theory of Teichmüller spaces. It is useful for graduate students and researchers in geometry, topology and analysis. Distributed within the Americas by the American Mathematical Society.