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Modern Approaches to Discrete Curvature

  • Laurent Najman
  • Pascal Romon

Part of the Lecture Notes in Mathematics book series (LNM, volume 2184)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Frank Bauer, Bobo Hua, Jürgen Jost, Shiping Liu, Guofang Wang
    Pages 1-62
  3. Facundo Mémoli
    Pages 115-132
  4. Frédéric Chazal, David Cohen-Steiner, André Lieutier, Quentin Mérigot, Boris Thibert
    Pages 133-158
  5. Alexander I. Bobenko, Ulrike Bücking, Stefan Sechelmann
    Pages 259-291
  6. Jacques-Olivier Lachaud, David Coeurjolly, Jérémy Levallois
    Pages 293-348
  7. Back Matter
    Pages 349-353

About this book

Introduction

 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.

Keywords

Discrete curvature Metric spaces Riemannian and Euclidean geometries Topology geometric measure theory partial differential equations calculus of variations gradient flows Spectral Analysis Graph theory 05CXX, 35Pxx, 49Q15,52B60,52B70,52CXX, 60XX, 65C18/68U05, 90BXX

Editors and affiliations

  • Laurent Najman
    • 1
  • Pascal Romon
    • 2
  1. 1.Laboratoire d’Informatique Gaspard MongeUniversité Paris-Est - ESIEE ParisNoisy-le-GrandFrance
  2. 2.Laboratoire d’Analyse et de Mathématiques AppliquéesUniversité Paris-Est Marne-la-ValléeMarne-la-ValléeFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-58002-9
  • Copyright Information The Editor(s) (if applicable) and The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-58001-2
  • Online ISBN 978-3-319-58002-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site