Differential Geometry in the Large (London Mathematical Society Lecture Note Series Book 463)

The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry. Contents List of Contributors Introduction Part One: Geometric Evolution Equations and Curvature Flow 1 Real Geometric Invariant Theory • C. Böhm and R.A. Lafuente 2 Convex Ancient Solutions to Mean Curvature Flow • T. Bourni, M. Langford and G. Tinaglia 3 Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings in Minkowski Space and the Cross Curvature Flow • P. Bryan, M. Ivaki and J. Scheuer 4 A Mean Curvature Flow for Conformally Compact Manifolds • A.R. Gover and V.-M. Wheeler 5 A Survey on the Ricci Flow on Singular Spaces • K. Kröncke and B. Vertman Part Two: Structures on Manifolds and Mathematical Physics 6 Some Open Problems in Sasaki Geometry • C. Boyer, H. Huang, E. Legendre and C. Tønnesen-Friedman 7 The Prescribed Ricci Curvature Problem for Homogeneous Metrics • T. Buttsworth and A. Pulemotov 8 Singular Yamabe and Obata Problems • A.R. Goverand A.K. Waldron 9 Einstein Metrics, Harmonic Forms and Conformally • Kähler Geometry C. LeBrun 10 Construction of the Supersymmetric Path Integral: A Survey • M. Ludewig 11 Tight Models of de-Rham Algebras of Highly Connected Manifolds • L. Schwachhöfer Part Three Recent Developments in Non-Negative Sectional Curvature 12 Fake Lens Spaces and Non-Negative Sectional Curvature • S. Goette, M. Kerin and K. Shankar 13 Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey • F. Galaz-García, L. Guijarro and J. Núñez-Zimbrón 14 Pseudo-Angle Systems and the Simplicial • Gauss–Bonnet–Chern Theorem S. Klaus 15 Aspects and Examples on Quantitative Stratification with Lower Curvature Bounds • N. Li 16 Universal Covers of Ricci Limit and RCD Spaces • J. Pan and G. Wei 17 Local and Global Homogeneity for Manifolds of Positive Curvature • J.A. Wolf "The 2019 'Australian-German Workshop on Differential Geometry in the Large' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry"--Provided by publisher A comprehensive tour across differential geometry, geometric analysis and differential topology, this graduate-level text touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry. A joy to the expert and novice alike From Ricci Flow To Git, Physics To Curvature Bounds, Sasaki Geometry To Almost Formality. This Is Differential Geometry At Large.