Lecture Notes in Mathematics

Modern Approaches to Discrete Curvature

Editors: Najman, Laurent, Romon, Pascal (Eds.)

  • A unique coherent glimpse of the state-of-the-art in Discrete CurvatureOf interest to both mathematicians and computer scientistsA vertiginous collection of ideas and tools

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About this book

 This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

Table of contents (9 chapters)

  • The Geometric Meaning of Curvature: Local and Nonlocal Aspects of Ricci Curvature

    Bauer, Frank (et al.)

    Pages 1-62

  • Metric Curvatures Revisited: A Brief Overview

    Saucan, Emil

    Pages 63-114

  • Distances Between Datasets

    Mémoli, Facundo

    Pages 115-132

  • Inference of Curvature Using Tubular Neighborhoods

    Chazal, Frédéric (et al.)

    Pages 133-158

  • Entropic Ricci Curvature for Discrete Spaces

    Maas, Jan

    Pages 159-174

Buy this book

eBook n/a
  • ISBN 978-3-319-58002-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-319-58001-2
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Modern Approaches to Discrete Curvature
Editors
  • Laurent Najman
  • Pascal Romon
Series Title
Lecture Notes in Mathematics
Series Volume
2184
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s)
eBook ISBN
978-3-319-58002-9
DOI
10.1007/978-3-319-58002-9
Softcover ISBN
978-3-319-58001-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXVI, 353
Number of Illustrations and Tables
45 b/w illustrations, 35 illustrations in colour
Topics