Constant mean curvature hypersurfaces condensing along a submanifold

2004/05/28 by Fethi Mahmoudi, Rafe Mazzeo, Mahmoudi, Fethi +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.math/0405564

arxiv created 2004/05/28 · arxiv updated 2009/12/01

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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