The Existence of G-Invariant constant mean curvature Hypersurfaces

Zhiang Wu; Tongrui Wang

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arXiv · 2103.16892

The Existence of G-Invariant constant mean curvature Hypersurfaces

Zhiang Wu·Tongrui Wang

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Abstract

In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\leq n+1\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. Suppose the union of non-principal orbits $M\setminus M^{reg}$ is a smooth embedded submanifold of $M$ without boundary and ${\rm dim}(M\setminus M^{reg})\leq n-2 $. Then for any $c\in\mathbb{R}$, we show the existence of a nontrivial, smooth, closed, $G$-equivariant almost embedded $G$-invariant hypersurface $\Sigma^n$ of constant mean curvature $c$.

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Zhiang Wu, Tongrui Wang. 2021-03-31. The Existence of G-Invariant constant mean curvature Hypersurfaces. https://arxiv.org/abs/2103.16892

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