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9780521592222

Comparison Geometry

by
  • ISBN13:

    9780521592222

  • ISBN10:

    0521592224

  • Format: Hardcover
  • Copyright: 1997-05-13
  • Publisher: Cambridge University Press

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Summary

This book documents the recent focus on a branch of Riemannian geometry called Comparison Geometry. The simple idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution recently. This volume is an up-to-date reflection of the recent development regarding spaces with lower (or two-sided) curvature bounds. The content reflects some of the most exciting activities in comparison geometry during the year and especially of the Mathematical Sciences Research Institute's workshop devoted to the subject. This volume features both survey and research articles. It also provides complete proofs: in one case, a new, unified strategy is presented and new proofs are offered. This volume will be a valuable source for advanced researchers and those who wish to learn about and contribute to this beautiful subject.

Table of Contents

Injectivity Radius Estimates and Sphere Theorems
1(48)
UWE ABRESCH
WOLFGANG T. MEYER
Scalar Curvature and Geometrization Conjectures for 3-Manifolds
49(34)
MICHAEL T. ANDERSON
Aspects of Ricci Curvature
83(16)
TOBIAS H. COLDING
A Genealogy of Noncompact Manifolds of Nonnegative Curvature: History and Logic
99(36)
ROBERT E. GREENE
Differential Geometric Aspects of Alexandrov Spaces
135(14)
YUKIO OTSU
Collapsing with No Proper Extremal Subsets
149(8)
G. PERELMAN
Construction of Manifolds of Positive Ricci Curvature with Big Volume and Large Betti Numbers
157(8)
G. PERELMAN
A Complete Riemannian Manifold of Positive Ricci Curvature with Euclidean Volume Growth and Nonunique Asymptotic Cone
165(2)
G. PERELMAN
Convergence Theorems in Riemannian Geometry
167(36)
PETER PETERSEN
Applications of Quasigeodesics and Gradient Curves
203(18)
ANTON PETRUNIN
The Comparison Geometry of Ricci Curvature
221
SHUNHUI ZHU

Supplemental Materials

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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