Dedication

pp v-vi

Contents

pp vii-xiv

List of Contributors

pp xv-xvi

Introduction

pp 1-8

Part One - Geometric Evolution Equations and Curvature Flow

pp 9-10

1 - Real Geometric Invariant Theory

pp 11-49

2 - Convex Ancient Solutions to Mean Curvature Flow

pp 50-74

3 - Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings in Minkowski Space and the Cross Curvature Flow

pp 75-97

4 - A Mean Curvature Flow for Conformally Compact Manifolds

pp 98-117

5 - A Survey on the Ricci Flow on Singular Spaces

pp 118-140

Part Two - Structures on Manifolds and Mathematical Physics

pp 141-142

6 - Some Open Problems in Sasaki Geometry

pp 143-168

7 - The Prescribed Ricci Curvature Problem for Homogeneous Metrics

pp 169-192

8 - Singular Yamabe and Obata Problems

pp 193-214

9 - Einstein Metrics, Harmonic Forms and Conformally Kähler Geometry

pp 215-240

10 - Construction of the Supersymmetric Path Integral: A Survey

pp 241-259

11 - Tight Models of de-Rham Algebras of Highly Connected Manifolds

pp 260-282

Part Three - Recent Developments in Non-Negative Sectional Curvature

pp 283-284

12 - Fake Lens Spaces and Non-Negative Sectional Curvature

pp 285-290

13 - Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey

pp 291-310

14 - Pseudo-Angle Systems and the SimplicialGauss–Bonnet–Chern Theorem

pp 311-325

15 - Aspects and Examples on Quantitative Stratification with Lower Curvature Bounds

pp 326-351

16 - Universal Covers of Ricci Limit and RCD Spaces

pp 352-372

17 - Local and Global Homogeneity for Manifolds of Positive Curvature

pp 373-384