Nonlocal Delaunay surfaces
Analysis of PDEs
2015-10-06 v2
Abstract
We construct codimension 1 surfaces of any dimension that minimize a periodic nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing. These surfaces may be seen as a nonlocal analogue of the classical Delaunay surfaces (onduloids). For small volume, most of their mass tends to be concentrated in a periodic array and the surfaces are close to a periodic array of balls (in fact, we give explicit quantitative bounds on these facts).
Cite
@article{arxiv.1501.07459,
title = {Nonlocal Delaunay surfaces},
author = {Juan Dávila and Manuel del Pino and Serena Dipierro and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1501.07459},
year = {2015}
}