04-13【张瑞珈】腾讯会议 几何分析相关讲座

发布者:卢珊珊发布时间:2021-04-07浏览次数:10

题目: Asymptotic convergence for a class of anisotropic curvature flows


报告人:张瑞珈 (清华大学)


时间:2021年4月13日(周二),19:30-21:00


腾讯会议ID: 972 825 228


报告摘要: 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 $k\geq2$, $0<\beta\leq 1$, $\alpha\geq \beta+k$,  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 $k \geq 2$.This is based on joint work with Haizhong Li and Botong Xu.


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