• Corpus ID: 203626772

Existence of multiple closed CMC hypersurfaces with small mean curvature

  title={Existence of multiple closed CMC hypersurfaces with small mean curvature},
  author={Akashdeep Dey},
  journal={arXiv: Differential Geometry},
  • Akashdeep Dey
  • Published 2 October 2019
  • Mathematics
  • arXiv: Differential Geometry
Let $(M^{n+1},g)$ be a closed Riemannian manifold, $n+1\geq 3$. We will prove that for all $m \in \mathbb{N}$, there exists $c^{*}(m)>0$, which depends on $g$, such that if $0 0$, there exist at least $\gamma_0c^{-\frac{1}{n+1}}$ many closed $c$-CMC hypersurfaces (with optimal regularity) in $(M,g)$. This extends the theorem of Zhou and Zhu, where they proved the existence of at least one closed $c$-CMC hypersurface in $(M,g)$. 
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