The Existence of Embedded $G$-Invariant Minimal Hypersurface

Zhenhua Liu

The Existence of Embedded $G$-Invariant Minimal Hypersurface

Differential Geometry 2020-07-07 v3

Authors: Zhenhua Liu

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.

Keywords

minimal hypersurface lie group action isometry cohomogeneity existence theorem

Cite

@article{arxiv.1812.02315,
  title  = {The Existence of Embedded $G$-Invariant Minimal Hypersurface},
  author = {Zhenhua Liu},
  journal= {arXiv preprint arXiv:1812.02315},
  year   = {2020}
}

Comments

Corrected a mistake pointed out by Antoine Song and added more proofs and discussions at the referee's suggestion. To appear in Calc. Var. Partial Differential Equations

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