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dc.contributor.authorCabré Vilagut, Xavier
dc.contributor.authorFall, Mouhamed Moustapha
dc.contributor.authorSolà-Morales Rubió, Joan de
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-02-13T09:10:01Z
dc.date.available2019-12-01T01:25:27Z
dc.date.issued2018-12-01
dc.identifier.citationCabre, X.; Fall, M.; Sola-morales, J. Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay. "Journal für die Reine und angewandte Mathematik", 1 Desembre 2018, vol. 2018, núm. 745, p. 253-280.
dc.identifier.issn0075-4102
dc.identifier.urihttp://hdl.handle.net/2117/129002
dc.description.abstractWe are concerned with hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are twofold. First we prove the nonlocal analogue of the Alexandrov result characterizing spheres as the only closed embedded hypersurfaces in RN with constant mean curvature. Here we use the moving planes method. Our second result establishes the existence of periodic bands or “cylinders” in R2 with constant nonlocal mean curvature and bifurcating from a straight band. These are Delaunay-type bands in the nonlocal setting. Here we use a Lyapunov–Schmidt procedure for a quasilinear type fractional elliptic equation.
dc.format.extent28 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshGeometry, Differencial
dc.subject.lcshCurves
dc.subject.lcshSurfaces
dc.titleCurves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay
dc.typeArticle
dc.subject.lemacGeometria diferencial
dc.subject.lemacCorbes
dc.subject.lemacSuperfícies
dc.contributor.groupUniversitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
dc.identifier.doi10.1515/crelle-2015-0117
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.degruyter.com/view/j/crll.ahead-of-print/crelle-2015-0117/crelle-2015-0117.xml
dc.rights.accessOpen Access
local.identifier.drac23617184
dc.description.versionPostprint (author's final draft)
local.citation.authorCabre, X.; Fall, M.; Sola-morales, J.
local.citation.publicationNameJournal für die Reine und angewandte Mathematik
local.citation.volume2018
local.citation.number745
local.citation.startingPage253
local.citation.endingPage280


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