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Advanced Courses in Mathematics - CRM Barcelona

Global Riemannian Geometry: Curvature and Topology

Authors: Hurtado, A., Markvorsen, S., Min-Oo, M., Palmer, V.

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  • 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
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About this Textbook

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.

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.

Table of contents (2 chapters)

Table of contents (2 chapters)
  • Distance Geometric Analysis on Manifolds

    Pages 1-81

    Hurtado, Ana (et al.)

  • The Dirac Operator in Geometry and Physics

    Pages 83-121

    Min-Oo, Maung

Buy this book

eBook $24.99
price for Mexico
  • ISBN 978-3-030-55293-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $32.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Global Riemannian Geometry: Curvature and Topology
Authors
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-55293-0
DOI
10.1007/978-3-030-55293-0
Softcover ISBN
978-3-030-55292-3
Series ISSN
2297-0304
Edition Number
2
Number of Pages
VII, 121
Number of Illustrations
1 b/w illustrations
Topics

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