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Birkhäuser

Global Riemannian Geometry: Curvature and Topology

  • Textbook
  • © 2020

Overview

Authors:
  1. Ana Hurtado

    1. Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain

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  2. Steen Markvorsen

    1. DTU Compute, Technical University of Denmark, Kgs. Lyngby, Denmark

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  3. Maung Min-Oo

    1. Department of Mathematics & Statistics, McMaster University, Hamilton, Canada

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  4. Vicente Palmer

    1. Departament de Matemàtiques, Universidad Jaume I, Castelló de la Plana, Spain

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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

Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-vii
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  2. Distance Geometric Analysis on Manifolds

    • Ana Hurtado, Steen Markvorsen, Vicente Palmer
    Pages 1-81

  3. The Dirac Operator in Geometry and Physics

    • Maung Min-Oo
    Pages 83-121
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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

  • Departamento de Geometría y Topología, Universidad de Granada, Granada, Spain

    Ana Hurtado

  • DTU Compute, Technical University of Denmark, Kgs. Lyngby, Denmark

    Steen Markvorsen

  • Department of Mathematics & Statistics, McMaster University, Hamilton, Canada

    Maung Min-Oo

  • Departament de Matemàtiques, Universidad Jaume I, Castelló de la Plana, Spain

    Vicente Palmer

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.

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