Differential Geometry in the Large
Published on 22. October 2020
Book
Paperback/Softback
398 pages
978-1-108-81281-8 (ISBN)
Description
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 Kaehler and Sasaki geometry.
Reviews / Votes
'The high-quality surveys and original work in this book give a convenient path to understand some recent exciting developments in global Differential Geometry and Geometric Analysis. This should be of great value to graduate students entering the field, as well as to more experienced researchers looking for an updated perspective on a wide range of topics, ranging from nonnegative curvature and Alexandrov spaces to geometric flows and equivariant geometry.' Renato G. Bettiol, Lehman College, The City University of New York '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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 226 mm
Width: 196 mm
Thickness: 20 mm
Weight
590 gr
ISBN-13
978-1-108-81281-8 (9781108812818)
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Schweitzer Classification
Persons
Content
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 Boehm 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 Kroencke 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. Tonnesen-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 Kaehler 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 Schwachhoefer; 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-Garcia, Luis Guijarro and Jesus Nunez-Zimbron; 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.