Multiply-periodic hypersurfaces with constant nonlocal mean curvature
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 10.

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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DOI : 10.1051/cocv/2019047
Classification : 47G20, 53A10, 35B10
Mots-clés : Fractional perimeter, non local mean curvature, bifurcation 
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     title = {Multiply-periodic hypersurfaces with constant nonlocal mean curvature},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
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Minlend, Ignace Aristide; Niang, Alassane; Thiam, El hadji Abdoulaye. Multiply-periodic hypersurfaces with constant nonlocal mean curvature. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 10. doi : 10.1051/cocv/2019047. http://www.numdam.org/articles/10.1051/cocv/2019047/

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