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- W4297778306 abstract "In this paper, by using new auxiliary functions, we study a class of contracting flows of closed, star-shaped hypersurfaces in $mathbb{R}^{n+1}$ with speed $r^{frac{alpha}{beta}}sigma_k^{frac{1}{beta}}$, where $sigma_k$ is the $k$-th elementary symmetric polynomial of the principal curvatures, $alpha$, $beta$ are positive constants and $r$ is the distance from points on the hypersurface to the origin. We obtain convergence results under some assumptions of $k$, $alpha$, $beta$. When $kgeq2$, $0<betaleq 1$, $alphageq beta+k$, we prove that the $k$-convex solution to the flow exists for all time and converges smoothly to a sphere after normalization, in particular, we generalize Li-Sheng-Wang's result from uniformly convex to $k$-convex. When $k geq 2$, $beta=k$, $alpha geq 2k$, we prove that the $k$-convex solution to the flow exists for all time and converges smoothly to a sphere after normalization, in particular, we generalize Ling Xiao's result from $k=2$ to $k geq 2$." @default.
- W4297778306 created "2022-10-01" @default.
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- W4297778306 date "2021-03-01" @default.
- W4297778306 modified "2023-10-14" @default.
- W4297778306 title "Asymptotic convergence for a class of anisotropic curvature flows" @default.
- W4297778306 doi "https://doi.org/10.48550/arxiv.2103.00842" @default.
- W4297778306 hasPublicationYear "2021" @default.
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