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Delaunay hypersurfaces with constant nonlocal mean curvature

Autor
Cabre, X.; Fall, M.; Weth, T.
Tipus d'activitat
Article en revista
Revista
Journal de mathématiques pures et appliquées
Data de publicació
2017-08-12
Volum
110
Pàgina inicial
32
Pàgina final
70
DOI
https://doi.org/10.1016/j.matpur.2017.07.005 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/111328 Obrir en finestra nova
URL
http://www.sciencedirect.com/science/article/pii/S0021782417300995?via%3Dihub Obrir en finestra nova
Resum
We study hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated with critical points of the fractional perimeter functional under a volume constraint. We establish the existence of a smooth branch of periodic cylinders in RN, N=2, all of them with the same constant nonlocal mean curvature, and bifurcating from a straight cylinder. These are Delaunay type cylinders in the nonlocal setting. The proof uses the Crandall-Rabinowitz theorem applied t...
Citació
Cabre, X., Fall, M., Weth, T. Delaunay hypersurfaces with constant nonlocal mean curvature. "Journal de mathématiques pures et appliquées", 12 Agost 2017, vol. 110, p.32-70.
Paraules clau
Constant nonlocal mean curvature, Delaunay periodic cylinders
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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