Multiply-periodic hypersurfaces with constant nonlocal mean curvature

Published 5 Apr 2018 in math.AP | (1804.01782v1)

Abstract: We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of smooth branches of multiply-periodic hypersurfaces bifurcating from suitable parallel hyperplanes.

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