Constant mean curvature hypersurfaces condensing along a submanifold
Differential Geometry
2007-05-23 v1
Abstract
Given any nondegenerate k-dimensional minimal submanifold K of codimension greater than 1, we prove the existence of families of constant mean curvature submanifolds, with mean curvature varying from one member of the family to another, which `condense' to K. In particular, our result proves the existence of constant mean curvature hypersurfaces with nontrivial topology in any Riemannian manifold.
Cite
@article{arxiv.math/0405564,
title = {Constant mean curvature hypersurfaces condensing along a submanifold},
author = {Fethi Mahmoudi and Rafe Mazzeo and Frank Pacard},
journal= {arXiv preprint arXiv:math/0405564},
year = {2007}
}