Metric Structures For Riemannian And Non Riemannian Spaces

Author : Mikhail Gromov
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 54,8 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9780817645830

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Metric Structures for Riemannian and Non-Riemannian Spaces by Mikhail Gromov Pdf

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Author : Mikhael Gromov
Publisher : Unknown
Page : 585 pages
File Size : 53,7 Mb
Release : 2001
Category : Riemannian manifolds
ISBN : OCLC:49611376

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Metric Structures for Riemannian and Non-Riemannian Spaces by Mikhael Gromov Pdf

Author : Mikhail Gromov
Publisher : Birkhäuser
Page : 586 pages
File Size : 49,5 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0817671447

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Metric Structures for Riemannian and Non-Riemannian Spaces by Mikhail Gromov Pdf

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Author : Mikhael Gromov
Publisher : Unknown
Page : 585 pages
File Size : 45,7 Mb
Release : 1998
Category : Riemannian manifolds
ISBN : OCLC:988818089

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Metric Structures for Riemannian and Non-Riemannian Spaces by Mikhael Gromov Pdf

Author : Takashi Shioya
Publisher : Unknown
Page : 0 pages
File Size : 52,7 Mb
Release : 2016
Category : Geometry, Differential
ISBN : 3037191589

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Metric Measure Geometry by Takashi Shioya Pdf

This book studies a new theory of metric geometry on metric measure spaces. The theory was originally developed by M. Gromov in his book Metric Structures for Riemannian and Non-Riemannian Spaces and based on the idea of the concentration of measure phenomenon by Levy and Milman. A central theme in this book is the study of the observable distance between metric measure spaces, defined by the difference between 1-Lipschitz functions on one space and those on the other. The topology on the set of metric measure spaces induced by the observable distance function is weaker than the measured Gromov-Hausdorff topology and allows the author to investigate a sequence of Riemannian manifolds with unbounded dimensions. One of the main parts of this presentation is the discussion of a natural compactification of the completion of the space of metric measure spaces. The stability of the curvature-dimension condition is also discussed.

Author : Lutz Habermann
Publisher : Springer
Page : 123 pages
File Size : 52,6 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540444435

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Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures by Lutz Habermann Pdf

This monograph deals with recent questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a new canonical metric for conformal structures. This book is accessible to readers with basic knowledge in differential geometry and global analysis. It addresses graduates and researchers.

Author : Martin R. Bridson,André Häfliger
Publisher : Springer Science & Business Media
Page : 665 pages
File Size : 41,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662124949

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Metric Spaces of Non-Positive Curvature by Martin R. Bridson,André Häfliger Pdf

A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

Author : Valerii Berestovskii,Yurii Nikonorov
Publisher : Springer Nature
Page : 482 pages
File Size : 41,6 Mb
Release : 2020-11-05
Category : Mathematics
ISBN : 9783030566586

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Riemannian Manifolds and Homogeneous Geodesics by Valerii Berestovskii,Yurii Nikonorov Pdf

This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.

Author : Wilderich Tuschmann,David J. Wraith
Publisher : Springer
Page : 123 pages
File Size : 46,5 Mb
Release : 2015-10-14
Category : Mathematics
ISBN : 9783034809481

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Moduli Spaces of Riemannian Metrics by Wilderich Tuschmann,David J. Wraith Pdf

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.

Author : Saminathan Ponnusamy,T. Sugawa,Matti Vuorinen
Publisher : Unknown
Page : 378 pages
File Size : 48,9 Mb
Release : 2007
Category : Mathematics
ISBN : PSU:000061002678

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Quasiconformal Mappings and Their Applications by Saminathan Ponnusamy,T. Sugawa,Matti Vuorinen Pdf

"Quasiconformal Mappings and their Applications covers conformal invariance and conformally invariant metrics, hyperbolic-type metrics and hyperbolic geodesics, isometries of relative metrics, uniform spaces and Gromov hyperbolicity, quasiregular mappings and quasiconformal mappings in n-space, universal Teichmuller space and related topics, quasiminimizers and potential theory, and numerical conformal mapping and circle packings."--BOOK JACKET.

Author : Anonim
Publisher : Unknown
Page : 632 pages
File Size : 50,9 Mb
Release : 2001
Category : Electronic journals
ISBN : UOM:39015053952878

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The Bulletin of Symbolic Logic by Anonim Pdf

Author : Athanase Papadopoulos
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 328 pages
File Size : 53,5 Mb
Release : 2014
Category : Convex domains
ISBN : 3037191325

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Metric Spaces, Convexity, and Non-positive Curvature by Athanase Papadopoulos Pdf

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

Author : Yurĭi Grigorevǐc Reshetnyak
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 54,6 Mb
Release : 1993-10-14
Category : Mathematics
ISBN : 3540547010

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Geometry IV by Yurĭi Grigorevǐc Reshetnyak Pdf

This book contains two surveys on modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. Coverage examines two-dimensional Riemannian manifolds of bounded curvature and metric spaces whose curvature lies between two given constants. This book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.

Author : Anonim
Publisher : Unknown
Page : 420 pages
File Size : 55,8 Mb
Release : 2005
Category : Communication
ISBN : UIUC:30112081594209

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Interdisciplinary Information Sciences by Anonim Pdf

Author : Royal Society of Edinburgh
Publisher : Unknown
Page : 690 pages
File Size : 50,9 Mb
Release : 1974
Category : Mathematics
ISBN : UCSC:32106018249661

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Proceedings by Royal Society of Edinburgh Pdf