Surveys in Differential Geometry, Vol. 11: Metric and Comparison Geometry

The works included in this new volume, edited by Jeffrey Cheeger and Karsten Grove, treat important recent developments in metric geometry and comparison geometry. Both these areas are vital and expanding components of modern geometrySurveys in Differential Geometry (SDG) is an annual collection of the invaluable talks given at the JDG conference, as well as of remarks from invited scholars. The series presents an overview of recent trends, while making predictions and suggestions for future research. The SDG series is a beneficial collection for experts and non-experts alike, and in particular, for those independent of the mainstream of activity in the field of geometry. Contents Collapsed Manifolds with Bounded Sectional Curvature and Applications Nonnegatively and Positively Curved Manifolds Examples of Manifolds with Non-negative Sectional Curvature Perelman's Stability Theorem Semiconcave Functions in Alexandrov's Geometry Manifolds with a lower Ricci Curvature Bound Optimal Transport and Ricci Curvature for Metric-Measure Spaces Manifolds of Positive Scalar Curvature: A Progress Report Spaces of Curvature Bounded Above Negative Curvature and Exotic Topology