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Nonlocal perimeter, curvature and minimal surfaces for measurable sets

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 curvatu...

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Detalles Bibliográficos
Autores principales: Mazón, José M, Rossi, Julio Daniel, Toledo, J Julián
Lenguaje:eng
Publicado: Springer 2019
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-06243-9
http://cds.cern.ch/record/2673412
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author Mazón, José M
Rossi, Julio Daniel
Toledo, J Julián
author_facet Mazón, José M
Rossi, Julio Daniel
Toledo, J Julián
author_sort Mazón, José M
collection CERN
description 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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institution Organización Europea para la Investigación Nuclear
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publishDate 2019
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spelling cern-26734122021-04-21T18:25:27Zdoi:10.1007/978-3-030-06243-9http://cds.cern.ch/record/2673412engMazón, José MRossi, Julio DanielToledo, J JuliánNonlocal perimeter, curvature and minimal surfaces for measurable setsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:26734122019
spellingShingle Mathematical Physics and Mathematics
Mazón, José M
Rossi, Julio Daniel
Toledo, J Julián
Nonlocal perimeter, curvature and minimal surfaces for measurable sets
title Nonlocal perimeter, curvature and minimal surfaces for measurable sets
title_full Nonlocal perimeter, curvature and minimal surfaces for measurable sets
title_fullStr Nonlocal perimeter, curvature and minimal surfaces for measurable sets
title_full_unstemmed Nonlocal perimeter, curvature and minimal surfaces for measurable sets
title_short Nonlocal perimeter, curvature and minimal surfaces for measurable sets
title_sort nonlocal perimeter, curvature and minimal surfaces for measurable sets
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-06243-9
http://cds.cern.ch/record/2673412
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AT rossijuliodaniel nonlocalperimetercurvatureandminimalsurfacesformeasurablesets
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