| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 10 | |
| Number of page(s) | 33 | |
| DOI | https://doi.org/10.1051/cocv/2019047 | |
| Published online | 14 February 2020 | |
Multiply-periodic hypersurfaces with constant nonlocal mean curvature
1
African Institute for Mathematical Sciences of Senegal,
KM 2,
Route de Joal,
B.P. 14 18.
Mbour, Senegal.
2
Cheikh Anta Diop University,
Cheikh Anta Diop Avenue,
B.P. 5005
Dakar-Fann, Senegal.
* Corresponding author: alassane4.niang@ucad.edu.sn
Received:
27
May
2018
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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