Constant mean curvature hypersurfaces condensing on a submanifold
Constant mean curvature hypersurfaces condensing on a submanifold
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DOI：
10.1007/s00039-006-0566-7
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发表时间：
2006-06
期刊：
影响因子：
--
通讯作者：
F. Mahmoudi;R. Mazzeo;F. Pacard
中科院分区：
文献类型：
--
作者：
F. Mahmoudi;R. Mazzeo;F. Pacard
给出余维数大于1的任意非退化K维极小子流形K，证明了具有平均曲率的常平均曲率子流形族的存在性，这些子流形族的平均曲率随族成员的不同而变化，并“压缩”为K。特别地，我们的结果证明了在任意黎曼流形中存在具有非平凡拓扑的常平均曲率超曲面。
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.