Existence of minimal hypersurfaces with non-empty free Boundary for generic metrics

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-09-04 DOI:10.1353/ajm.2022.0012

Zhichao Wang

引用次数: 2

Abstract

abstract:For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a compact manifold with boundary $(M^{n+1},\break\partial M)$, $3\leq (n+1)\leq 7$, we prove that, for any open subset $V$ of $\partial M$, there exists a compact, properly embedded free boundary minimal hypersurface intersecting $V$.

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一般度量的非空自由边界极小超曲面的存在性

对于边界为$(M^{n+1},\break\partial M)$, $3\leq (n+1)\leq 7$的紧致流形上的几乎所有($C^\infty$ Baire意义上的)黎曼度量，我们证明了对于$\partial M$的任意开子集$V$，存在与$V$相交的紧致的、适当嵌入的自由边界极小超曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.