Metric Diffusion Along Foliations

  • Szymon M. Walczak

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Szymon M. Walczak
    Pages 1-10
  3. Szymon M. Walczak
    Pages 11-20
  4. Szymon M. Walczak
    Pages 21-29
  5. Szymon M. Walczak
    Pages 31-48
  6. Back Matter
    Pages 53-55

About this book

Introduction

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.

Keywords

Wasserstein distance Metric diffusion Compact foliations heat diffusion non-compact foliations Holonomy Optimal Transportation Problem Harmonic measures

Authors and affiliations

  • Szymon M. Walczak
    • 1
  1. 1.National Science CenterKrakówPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-57517-9
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-57516-2
  • Online ISBN 978-3-319-57517-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book