Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds
Abstract
Given a domain $\Omega$ of $\mathbb{R}^{m+1}$ and a $k$dimensional nondegenerate minimal submanifold $K$ of $\pa \Omega$ with $1\le k\le m1$, we prove the existence of a family of embedded constant mean curvature hypersurfaces which as their mean curvature tends to infinity concentrate along $K$ and intersecting $\partial \Omega$ perpendicularly.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2146
 Bibcode:
 2007arXiv0711.2146M
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Differential Geometry;
 53A10;
 53C21;
 35R35
 EPrint:
 28 pages