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Título:	Curves and surfaces with constant nonlocal mean curvature: Meeting Alexandrov and Delaunay
Autor/a:	Cabré Vilagut, Xavier; Fall, Mouhamed Moustapha; Solà-Morales Rubió, Joan de
Otros autores:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
Abstract:	We 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.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Geometry, Differencial -Curves -Surfaces -Geometria diferencial -Corbes -Superfícies
Derechos:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión presentada Artículo
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