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- W2155598519 abstract "We are concerned with hypersurfaces of $mathbb{R}^N$ 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 $mathbb{R}^N$ with constant mean curvature. Here we use the moving planes method. Our second result establishes the existence of periodic bands or cylinders in $mathbb{R}^2$ 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." @default.
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- W2155598519 date "2015-03-02" @default.
- W2155598519 modified "2023-10-16" @default.
- W2155598519 title "Curves and surfaces with constant nonlocal mean curvature: meeting Alexandrov and Delaunay" @default.
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