English

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.

Keywords

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}
}
R2 v1 2026-07-22T17:06:03.360Z