Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets

 
 
Birkhäuser (Verlag)
  • erschienen am 10. Mai 2019
 
  • Buch
  • |
  • Softcover
  • |
  • XVIII, 123 Seiten
978-3-030-06242-2 (ISBN)
 
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.
Book
2019
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • 1 s/w Abbildung, 1 farbige Abbildung
  • |
  • Bibliographie
  • Höhe: 238 mm
  • |
  • Breite: 167 mm
  • |
  • Dicke: 12 mm
  • 268 gr
978-3-030-06242-2 (9783030062422)
10.1007/978-3-030-06243-9
weitere Ausgaben werden ermittelt
Nonlocal Perimeter.- Nonlocal Isoperimetric Inequality.- Nonlocal Minimal Surfaces and Nonlocal Curvature.- Nonlocal Operators.- Nonlocal Cheeger and Calibrable Sets.- Nonlocal Heat Content.- A Nonlocal Mean Curvature Flow.- Bibliography.- Index.
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.
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