Differential Geometry in the Large

From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.

Owen Dearricott (Edited by), Wilderich Tuschmann (Edited by), Yuri Nikolayevsky (Edited by), Thomas Leistner (Edited by), Diarmuid Crowley (Edited by)

9781108812818, Cambridge University Press

Paperback / softback, published 22 October 2020

398 pages
22.8 x 15.2 x 2.3 cm, 0.58 kg

'The volume includes important additions to the literature including new results, new proofs of previous results, and simplified expositions, and also an excellent collection of surveys on recent activity. It is well written and offers a generous overview and invitation to a variety of modern, active topics in differential geometry.' Christopher Seaton, MAA Reviews

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.

Introduction Owen Dearricott, Wilderich Tuschmann, Yuri Nikolayevsky, Thomas Leistner and Diarmuid Crowley
Part I. Geometric Evolution Equations and Curvature Flow: 1. Real geometric invariant theory Christoph Böhm and Ramiro A. Lafuente
2. Convex ancient solutions to mean curvature flow Theodora Bourni, Mat Langford and Giuseppe Tinaglia
3. Negatively curved three-manifolds, hyperbolic metrics, isometric embeddings in Minkowski space and the cross curvature flow Paul Bryan, Mohammad N. Ivaki and Julian Scheuer
4. A mean curvature flow for conformally compact manifolds A. Rod Gover and Valentina-Mira Wheeler
5. A survey on the Ricci flow on singular spaces Klaus Kröncke and Boris Vertman
Part II. Structures on Manifolds and Mathematical Physics: 6. Some open problems in Sasaki geometry Charles P. Boyer, Hongnian Huang, Eveline Legendre and Christina W. Tønnesen-Friedman
7. The prescribed Ricci curvature problem for homogeneous metrics Timothy Buttsworth and Artem Pulemotov
8. Singular Yamabe and Obata problems A. Rod Gover and Andrew K. Waldron
9. Einstein metrics, harmonic forms and conformally Kähler geometry Claude LeBrun
10. Construction of the supersymmetric path integral: a survey Matthias Ludewig
11. Tight models of de-Rham algebras of highly connected manifolds Lorenz Schwachhöfer
Part III. Recent Developments in Non-Negative Sectional Curvature: 12. Fake lens spaces and non-negative sectional curvature Sebastian Goette, Martin Kerin and Krishnan Shankar
13. Collapsed three-dimensional Alexandrov spaces: a brief survey Fernando Galaz-García, Luis Guijarro and Jesús Núñez-Zimbrón
14. Pseudo-angle systems and the simplicial Gauss–Bonnet–Chern theorem Stephan Klaus
15. Aspects and examples on quantitative stratification with lower curvature bounds Nan Li
16. Universal covers of Ricci limit and RCD spaces Jiayin Pan and Guofang Wei
17. Local and global homogeneity for manifolds of positive curvature Joseph A. Wolf.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Algebraic topology [PBPD], Algebraic geometry [PBMW], Differential & Riemannian geometry [PBMP]