Calculus of Variations and Geometric Measure Theory

I. A. Minlend - A. Niang - E. H. A. Thiam

Multiply-periodic hypersurfaces with constant nonlocal mean curvature

created by niang on 25 Jul 2019
modified on 26 Jul 2019

[BibTeX]

Accepted Paper

Inserted: 25 jul 2019
Last Updated: 26 jul 2019

Journal: ESAIM : COCV
Pages: 36
Year: 2019

ArXiv: 1804.01782 PDF
Links: African Institute for Mathematical Sciences

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.