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- W3048651886 abstract "In this paper, we study the flow of closed, starshaped hypersurfaces in $mathbb{R}^{n+1}$ with speed $r^alphasigma_2^{1/2},$ where $sigma_2^{1/2}$ is the normalized square root of the scalar curvature, $alphageq 2,$ and $r$ is the distance from points on the hypersurface to the origin. We prove that the flow exists for all time and the starshapedness is preserved. Moreover, after normalization, we show that the flow converges exponentially fast to a sphere centered at origin. When $alpha<2,$ a counterexample is given for the above convergence." @default.
- W3048651886 created "2020-08-18" @default.
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- W3048651886 date "2023-01-01" @default.
- W3048651886 modified "2023-09-26" @default.
- W3048651886 title "Asymptotic convergence for modified scalar curvature flow" @default.
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- W3048651886 doi "https://doi.org/10.4310/cag.2023.v31.n1.a3" @default.
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