Multiply-periodic hypersurfaces with constant nonlocal mean curvature

Multiply-periodic hypersurfaces with constant nonlocal mean curvature

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 bifurcatin...

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Veröffentlicht in:ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2020, Vol.26, p.10
Hauptverfasser: Minlend, Ignace Aristide, Niang, Alassane, Thiam, El hadji Abdoulaye
Format: Artikel
Sprache:eng
Schlagworte:
Critical point
Curvature
Euclidean geometry
Euclidean space
Hyperplanes
Hyperspaces
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Zusammenfassung: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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2019047