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Metric Spaces, Convexity and Nonpositive Curvature
IRMA Lectures in Mathematics and Theoretical Physics Vol. 6

Athanase Papadopoulos (IRMA, Strasbourg, France)

Metric Spaces, Convexity and Nonpositive Curvature

Second edition

ISBN print 978-3-03719-132-3, ISBN online 978-3-03719-632-8
DOI 10.4171/132
January 2014, 320 pages, softcover, 17 x 24 cm.
48.00 Euro

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. It 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.

Further Information

Review of 1st ed. in Bull. Amer. Math. Soc. 43 (2006), 435–438

Review of 1st ed. in Internat. Math. News 204 (2007), 47–48

Review of 1st ed. in Jahresbericht der DMV 108 (2008), 61–62

Review of 1st ed. in Zentralblatt MATH 1115.53002

Review of 1st ed. in MR 2132506 (2005k:53042)

Review in Zentralblatt MATH 1296.53007