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Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets

  • José M. Mazón
  • Julio Daniel Rossi
  • J. Julián Toledo
Book

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 1-17
  3. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 19-28
  4. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 29-44
  5. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 45-52
  6. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 53-80
  7. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 81-106
  8. José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
    Pages 107-118
  9. Back Matter
    Pages 119-123

About this book

Introduction

This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them. 

These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained. 

Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.

Keywords

sets of finite perimeter nonlocal operators cheeger sets calibrable sets heat content nonlocal evolution problems non-singular kernels

Authors and affiliations

  • José M. Mazón
    • 1
  • Julio Daniel Rossi
    • 2
  • J. Julián Toledo
    • 3
  1. 1.Departamento de Análisis MatemáticoUniversitat de ValènciaValenciaSpain
  2. 2.Departamento de MatemáticasUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.Departamento de Análisis MatemáticoUniversitat de ValènciaValènciaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-06243-9
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-06242-2
  • Online ISBN 978-3-030-06243-9
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site
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