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Uniqueness of closed self-similar solutions to $/sigma_k^{/alpha}$-curvature flow
发布时间: 2017-06-05     08:44   【返回上一页】 发布人:马辉


 北京师范大学数学科学学院

 

周五公众报告

 

 

 

报告题目:Uniqueness of closed self-similar solutions to $/sigma_k^{/alpha}$-curvature flow

 

 

报告人: 马辉 教授

 

(清华大学)

 


时间地点:201769日下午3:00-4:00, 后主楼1220


 

邀请人:葛建全 教授 

 

 

报告摘要: By adapting the test functions introduced by Choi-Daskaspoulos and Brendle-Choi-Daskaspoulos and exploring properties of the $k$-th elementary symmetric functions $/sigma_{k}$ intensively,  we show that for any fixed $k$ with $1/leq k/leq n-1$, any strictly convex closed hypersurface in $/mathbb{R}^{n+1}$ satisfying $/sigma_{k}^{/alpha}=/langle X,/nu /rangle$, with $/alpha/geq /frac{1}{k}$, must be a round sphere. In fact, we prove a uniqueness result for any strictly convex closed hypersurface in $/mathbb{R}^{n+1}$ satisfying $F+C=/langle X,/nu /rangle$, where $F$ is a positive homogeneous smooth symmetric function of the principal curvatures and $C$ is constant. The talk is based on the joint work with Shanze Gao and Haizhong Li.  

 

 

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