Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere

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dc.creatorCheng, Qing-Ming
dc.creatorLi, Haizhong
dc.creatorWei, Guoxin
dc.date2009-04-02
dc.date.accessioned2026-07-07T12:59:31Z
dc.date.available2026-07-07T12:59:31Z
dc.descriptionIn this paper, we study $n$-dimensional hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere $S^{n+1}(1)$ and construct many compact nontrivial embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature $H_m>0$ in $S^{n+1}(1)$, for $1\leq m\leq n-1$. In particular, if the $4^{\text{th}}$ mean curvature $H_4$ takes value between $\dfrac{1}{(\tan \fracπ{k})^4}$ and $\dfrac{k^4-4}{n(n-4)}$ for any integer $k\geq3$, then there exists an $n$-dimensional ($n\geq 5$) compact nontrivial embedded hypersurface with constant $H_4$ in $S^{n+1}(1)$.
dc.identifierhttps://arxiv.org/abs/0904.0299
dc.identifierhttp://arxiv.org/abs/0904.0299
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225597
dc.subjectDifferential Geometry
dc.titleEmbedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere
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