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Metric spaces, convexity and nonpositive curvature

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Published by European Mathematical Society in Zürich .
Written in English

Subjects:

  • Metric spaces,
  • Convex domains,
  • Curvature,
  • Geodesics (Mathematics),
  • Espaces métriques,
  • Algèbres convexes,
  • Courbure,
  • Géodésiques (Mathématiques)

Book details:

Edition Notes

Includes bibliographical references (p. [275]-282) and index.

StatementAthanase Papadopoulos.
SeriesIRMA lectures in mathematics and theoretical physics -- 6
Classifications
LC ClassificationsQA611.28 .P36 2005
The Physical Object
Paginationxi, 287 p. :
Number of Pages287
ID Numbers
Open LibraryOL17909932M
ISBN 103037190108
LC Control Number2006355594

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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.". Abstract 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. This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function is convex. We have also included a systematic introduction to the theory of geodesics and related matters in metric spaces, as well as a detailed presentation of a few facets of convexity theory that are useful in.   The purpose of this book is to describe the global properties of complete simply connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of 5/5(1).

  Prices (including delivery) for Metric Spaces, Convexity and Nonpositive CurvatureIRMA Lectures in Mathematics and Theoretical Ph by Athanase Papadopoulos. ISBN: Would you like to visit Booko United States? (You can change region by clicking the flag in the toolbar.)Released on: Decem Metric spaces, convexity, and nonpositive curvature, by Athanase Papadopoulos, European Math. Soc., Z¨urich, , xii + pp., EUR , ISBN Let us begin by recalling a few basic concepts. A metric space is a nonempty set M together with a nonnegative real-valued distance function d(x,y) defined for. 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. Alexandrov defines a metric space to be of curvature ≤κ if each point of the space has a neighbourhood which, equipped with the induced metric, is a CAT(κ) space. He and the Russian school which he founded have made an extensive study of the local properties of such spaces. A complete Riemannian manifold has curvature.

The purpose of this book is to describe the global properties of complete simply­ connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined. The new edition is an expanded and revised version. The book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function is : Athanase Papadopoulos. By Athanase Papadopoulos. This ebook covers metric areas of nonpositive curvature within the experience of Busemann, that's, metric areas whose distance functionality satisfies a convexity. additionally contained is a scientific advent to the speculation of geodesics in addition to a close presentation of a few features of convexity thought, that are worthwhile within the learn of nonpositive /5(9).   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.