The Existence of Embedded $G$-Invariant Minimal Hypersurface

Zhenhua Liu

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arXiv · 1812.02315

The Existence of Embedded $G$-Invariant Minimal Hypersurface

Zhenhua Liu

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Abstract

For a compact connected Lie group $G$ acting as isometries on a compact orientable Riemannian manifold $M^{n+1},$ and cohomogeneity not equal to 0 or 2, we prove the existence of a nontrivial embedded $G$-invariant minimal hypersurface, that is smooth outside a set of Hausdorff dimension at most $n-7.

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Zhenhua Liu. 2018-12-04. The Existence of Embedded $G$-Invariant Minimal Hypersurface. https://arxiv.org/abs/1812.02315

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