Metric structures for Riemannian and non-Riemannian spaces

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Metric structures for Riemannian and non-Riemannian spaces / Misha Gromov ; with appendices by M. Katz, P. Pansu, and S. Semmes ; English translation by Sean Michael Bates

資料種別:: 図書
出版情報:: Boston : Birkhäuser, c1999
形態:: xix, 585 p. ; 24 cm
シリーズ名:: Progress in mathematics ; v. 152 <BA00018010>
著者名:: Gromov, Mikhael, 1943- <DA00396717>
ISBN:: 9780817638986 [0817638989] (: Boston)
9783764338985 [3764338989] (: Basel)
書誌ID:: BA42350239

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その他の標題:

Structures métriques des variétés Riemanniennes

注記:

"Based on Structures métriques des variétés riemanniennes."
Editors of original French ed.: J. LaFontaine and P. Pansu
"This book arose from a course given at the University of Paris VII during the third trimester of 1979."--Pref. to French ed
Includes bibliographical references (p. [545]-574) and index

主題:

Riemannian manifolds

言語:

英語

目次情報:

Preface to the French Edition

Preface to the English Edition

Introduction: Metrics Everywhere

Length structures: Path metric spaces / 1：

Examples of path metric spaces

Arc-wise isometries

Degree and dilatation / 2：

Review : Degree of mappings between oriented manifolds

Elementary properties of dilatations for spheres

Some general homotopy counting results for Lipschitz maps

Dilatation of sphere-valued mappings

Metric structures / 3：

Lipschitz distance

Hausdorff distance

First examples of Hausdorff convergence

The noncompact case : Pointed distances

The Hausdorff-Lipschitz metric and quasi-isometry

First-order metric invariants and ultralimits

Convergence with control

Convergence and concentration of metric and measures

Loewner rediscovered: First, some history (in dimension 2) / 4：

Next, some questions in dimension Ã‡ 3

Finally, the theorems

An application of geometric integration theory

Unstable systolic inequalities and filling

Finer inequalities and systoles of universal spaces

Manifolds with bounded Ricci curvature / 5：

Precompactness

Growth of fundamental groups

The first Betti number

Small loops

Isoperimetric inequalities and amenability / 6：

Quasiregular mappings

Isoperimetric dimension of a manifold

Computations of isoperimetric dimension

Generalizations

Morse theory and minimal models / 7：

Application to Morse theory to loop spaces

Dilatation of mappings between simply connected manifolds

Pinching and collapse / 8：

Why pinch the sectional curvature?

Implications of pinched curvature

limits of pinched manifolds

Nilpotent groups

"Quasiconvex" domains in R[superscript n] / Appendix A：

Metric spaces and mappings seen at many scales / Appen B：

Basic concepts and examples

Analysis on general spaces

Rigidity and structure

An introduction to real-variable methods

Paul Levy's isoperimetric inequality / Appen C：

Systolically Free Manifolds / Appen D：

Bibliography

Glossary of Notation

Index

Preface to the French Edition

Preface to the English Edition

Introduction: Metrics Everywhere

Length structures: Path metric spaces / 1：

Examples of path metric spaces

Arc-wise isometries

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