Volume 26, 2020
|Number of page(s)||33|
|Published online||14 February 2020|
Multiply-periodic hypersurfaces with constant nonlocal mean curvature
African Institute for Mathematical Sciences of Senegal,
Route de Joal,
B.P. 14 18.
2 Cheikh Anta Diop University, Cheikh Anta Diop Avenue, B.P. 5005 Dakar-Fann, Senegal.
* Corresponding author: firstname.lastname@example.org
Accepted: 25 July 2019
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.
Mathematics Subject Classification: 47G20 / 53A10 / 35B10
Key words: Fractional perimeter / non local mean curvature / bifurcation
© EDP Sciences, SMAI 2020
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