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- W4308166301 abstract "In the present paper, we first establish and verify a new sharp hyperbolic version of the Michael-Simon inequality for mean curvatures in hyperbolic space $mathbb{H}^{n+1}$ based on the locally constrained inverse curvature flow introduced by Brendle, Guan and Li, provided that $M$ is $h$-convex and $f$ is a positive smooth function, where $lambda^{'}(r)=rm{cosh}$$r$. In particular, when $f$ is of constant, (0.1) coincides with the Minkowski type inequality stated by Brendle, Hung, and Wang. Further, we also establish and confirm a new sharp Michael-Simon inequality for the $k$-th mean curvatures in $mathbb{H}^{n+1}$ by virtue of the Brendle-Guan-Li's flow, provided that $M$ is $h$-convex and $Omega$ is the domain enclosed by $M$. In particular, when $f$ is of constant and $k$ is odd, (0.2) is exactly the weighted Alexandrov-Fenchel inequalities proven by Hu, Li, and Wei." @default.
- W4308166301 created "2022-11-08" @default.
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- W4308166301 date "2022-11-01" @default.
- W4308166301 modified "2023-09-26" @default.
- W4308166301 title "Michael-Simon type inequalities in hyperbolic space" @default.
- W4308166301 doi "https://doi.org/10.48550/arxiv.2211.00855" @default.
- W4308166301 hasPublicationYear "2022" @default.
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