Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds

Details Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds

2007-11-14

arxiv.org/abs/0711.2146v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

Given a domain $\Omega$ of $\mathbb{R}^{m+1}$ and a $k$-dimensional
non-degenerate minimal submanifold $K$ of $\pa \Omega$ with $1\le k\le m-1$, 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.

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