关于任意大面积和莫尔斯指数的极小超曲面的存在性

Geometry & Topology Pub Date : 2020-01-21 DOI:10.2140/gt.2022.26.2713

Yangyang Li

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引用次数: 5

摘要

我们证明了凹凸不平的封闭黎曼流形$(M^{n+1}, g)$$(3 \leq n+1 \leq 7)$允许一系列连通的封闭嵌入的双面极小超曲面，其面积和摩尔斯指数都趋于无穷。这改进了O. Chodosh和C. Mantoulidis先前关于任意大面积连通极小超曲面的结果。

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On the existence of minimal hypersurfaces with arbitrarily large area and Morse index

We show that a bumpy closed Riemannian manifold $(M^{n+1}, g)$ $(3 \leq n+1 \leq 7)$ admits a sequence of connected closed embedded two-sided minimal hypersurfaces whose areas and Morse indices both tend to infinity. This improves a previous result by O. Chodosh and C. Mantoulidis on connected minimal hypersurfaces with arbitrarily large area.

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来源期刊

Geometry & Topology

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