CMC hypersurface with finite index in hyperbolic space $\mathbb{H}^4$
2024
Online
report
In this paper, we prove that there are no complete noncompact constant mean curvature hypersurfaces with the mean curvature $H>1$ and finite index satisfying universal subexponential end growth in hyperbolic space $\mathbb{H}^4$. A more general nonexistence result can be proved in a $4$-dimensional Riemannian manifold with certain curvature conditions. We also show that $4$-manifold with $\operatorname{Ric}>1$ does not contain any complete noncompact stable minimal hypersurface with universal subexponential end growth. The proof relies on the harmonic function theory developed by Li-Tam-Wang and the $\mu$-bubble initially introduced by Gromov and further developed by Chodosh-Li-Stryker in the context of stable minimal hypersurfaces.
Comment: An extra condition is added in the main theorem. A second theorem is added. Proof slightly changed. References updated
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CMC hypersurface with finite index in hyperbolic space $\mathbb{H}^4$
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Autor/in / Beteiligte Person: | Hong, Han |
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Veröffentlichung: | 2024 |
Medientyp: | report |
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