Surveys in Differential Geometry

Preface

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