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Metric Diffusion Along Foliations

  • Book
  • © 2017

Overview

Authors:
  1. Szymon M. Walczak

    1. National Science Center, Kraków, Poland

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  • Covers metric diffusion along compact foliations
  • Reinforces basic principles in foliations, holonomy, and heat diffusion
  • Clarifies the metrization of weak topology
  • Includes supplementary material: sn.pub/extras
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Wasserstein Distance

    • Szymon M. Walczak
    Pages 1-10

  3. Foliations and Heat Diffusion

    • Szymon M. Walczak
    Pages 11-20

  4. Compact Foliations

    • Szymon M. Walczak
    Pages 21-29

  5. Metric Diffusion

    • Szymon M. Walczak
    Pages 31-48

  6. Metric Diffusion for Non-compact Foliations: Remarks

    • Szymon M. Walczak
    Pages 49-52

  7. Back Matter

    Pages 53-55
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Keywords

About this book

Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding.

Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.

Reviews

“The present book is a beautiful sample of results that can be proved on foliated manifolds by the theory of metric diffusion. … Graduate students and researchers in geometry, topology and dynamics of foliations will find this book especially valuable as it presents facts about the metric diffusion at the cutting edge of research.” (Glen E. Wheeler, Mathematical Reviews, May, 2018)

Authors and Affiliations

  • National Science Center, Kraków, Poland

    Szymon M. Walczak

Bibliographic Information

  • Book Title: Metric Diffusion Along Foliations

  • Authors: Szymon M. Walczak

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-57517-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s) 2017

  • Softcover ISBN: 978-3-319-57516-2Published: 24 May 2017

  • eBook ISBN: 978-3-319-57517-9Published: 16 May 2017

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XI, 55

  • Number of Illustrations: 19 b/w illustrations

  • Topics: Topology, Differential Geometry

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