Overview
- Discussion of the Laplacian as a 'swift' operator on minimal submanifolds in ambient spaces with small sectional curvatures
- Use of Dirac operators for general relativity
- Contains a clear exposition of contemporary topics in modern differential geometry
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (2 chapters)
Keywords
About this book
This book contains a clear exposition of two contemporary topics in modern differential geometry:
- distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature
- the study of scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator
It is intended for both graduate students and researchers.
This second edition has been updated to include recent developments such as promising results concerning the geometry of exit time moment spectra and potential analysis in weighted Riemannian manifolds, as well as results pertaining to an early conjecture on the geometry of the scalar curvature and speculations on new geometric approaches to the Index Theorem.
Authors and Affiliations
About the authors
Ana Hurtado is a professor at the Universidad de Granada.
Steen Markvorsen is a professor at the Technical University of Denmark.
Maung Min-Oo is emeritus professor at the McMaster University.
Vicente Palmer is a professor of Geometry at the University Jaume I.
Bibliographic Information
Book Title: Global Riemannian Geometry: Curvature and Topology
Authors: Ana Hurtado, Steen Markvorsen, Maung Min-Oo, Vicente Palmer
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-030-55293-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-55292-3Published: 20 August 2020
eBook ISBN: 978-3-030-55293-0Published: 19 August 2020
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 2
Number of Pages: VII, 121
Number of Illustrations: 1 b/w illustrations
Topics: Global Analysis and Analysis on Manifolds, Differential Geometry, Manifolds and Cell Complexes (incl. Diff.Topology)