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.
Author(s): Karsten Grove, Peter Petersen
Series: MSRI
Publisher: CUP
Year: 1997
Language: English
Pages: 261
TOC
......Page 1
000-preface......Page 2
001-Abresch - Injectivity Radius Estimates and Sphere Theorems......Page 4
049-Anderson - Scalar Curvature and Geometrization Conjectures for 3-Manifolds......Page 51
083-Colding - Aspects of Ricci Curvature......Page 85
099-Greene - A Genealogy of Noncompact Manifolds of Nonnegative Curvature......Page 101
135-Otsu - Differential Geometric Aspects of Alexandrov Spaces......Page 137
149-Perelman - Construction of Manifolds of Positive Ricci Curvature with Big Volume and Large Betti Numbers......Page 151
157-Perelman - Collapsing with No Proper Extremal Subsets......Page 158
165-Perelman - Example of a Complete Riemannian Manifold of Positive Ricci Curvature with Euclidean Volume Growth......Page 165
167-Petersen - Convergence Theorems in Riemannian Geometry......Page 167
203-Petrunin - Applications of Quasigeodesics and Gradient Curves......Page 203
221-Zhu - The Comparison Geometry of Ricci Curvature......Page 220
