Synopses & Reviews
This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.
Synopsis
This book documents the recent focus on a branch of Riemannian geometry called Comparison Geometry. The idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution of late. This volume is an up to date reflection of the recent development regarding spaces with lower or two-sided curvature bounds. It was developed from the Mathematical Sciences Research Instituteâs workshop devoted to the subject, and features both survey and research articles.
Table of Contents
1. Scalar curvature and geometrization conjectures for 3-manifolds Michael T. Anderson; 2. Injectivity radius estimates and sphere theorems Uwe Abresch and Wolfgang T. Meyer; 3. Aspects of Ricci curvature Tobias H. Colding; 4. A genealogy of noncompact manifolds of nonnegative curvature: history and logic R. E. Greene; 5. Differential geometric aspects of Alexandrov spaces Yukio Otsu; 6. Convergence theorems in Riemannian geometry Peter Petersen; 7. The comparison geometry of Ricci curvature Shunhui Zhu; 8. Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers G. Perelman; 9. Collapsing with no proper extremal subsets G. Perelman; 10. Example of a complete Riemannian manifold of positive Ricci curvature with Euclidean volume growth and with nonunique asymptotic cone G. Perelman; 11. Applications of quasigeodesics and gradient curves Anton Petrunin.