Existence of minimal hypersurfaces in complete manifolds of finite volume
Existence of minimal hypersurfaces in complete manifolds of finite volume
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DOI：
10.1007/s00222-019-00903-3
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发表时间：
2016-09
影响因子：
3.1
通讯作者：
Gregory R. Chambers;Yevgeny Liokumovich
中科院分区：
文献类型：
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作者：
Gregory R. Chambers;Yevgeny Liokumovich
证明了有限体积的完备非紧流形包含一个（可能是非紧的）有限体积的极小超曲面。主要的工具是下面的独立感兴趣的结果：如果一个区域U可以被一个族的超曲面扫出体积至多V，那么它可以被一个族的相互不相交的超曲面扫出体积至多。
We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a regionUcan be swept out by a family of hypersurfaces of volume at mostV, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most.