Higher codimension isoperimetric problems
Differential Geometry
2015-02-25 v1 Analysis of PDEs
Abstract
We consider a variational problem for submanifolds Q M with nonempty boundary Q = K. We propose the definition that the boundary K of any critical point Q have constant mean curvature, which seems to be a new perspective when dim Q \textless{} dim M . We then construct small nearly-spherical solutions of this higher codimension CMC prob-lem; these concentrate near the critical points of a certain curvature function.
Cite
@article{arxiv.1502.06746,
title = {Higher codimension isoperimetric problems},
author = {Rafe Mazzeo and Frank Pacard and Tatiana Zolotareva},
journal= {arXiv preprint arXiv:1502.06746},
year = {2015}
}