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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...
Autores principales: | , , |
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Lenguaje: | eng |
Publicado: |
Springer
2019
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1007/978-3-030-06243-9 http://cds.cern.ch/record/2673412 |
_version_ | 1780962496940605440 |
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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. |
id | cern-2673412 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2019 |
publisher | Springer |
record_format | invenio |
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 |
work_keys_str_mv | AT mazonjosem nonlocalperimetercurvatureandminimalsurfacesformeasurablesets AT rossijuliodaniel nonlocalperimetercurvatureandminimalsurfacesformeasurablesets AT toledojjulian nonlocalperimetercurvatureandminimalsurfacesformeasurablesets |