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Constant mean curvature hypersurfaces condensing along a submanifold

Fethi Mahmoudi·Rafe Mazzeo·Frank Pacard
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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.

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Fethi Mahmoudi, Rafe Mazzeo, Frank Pacard. 2004-05-28. Constant mean curvature hypersurfaces condensing along a submanifold. https://arxiv.org/abs/math/0405564

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