Minkowski type inequalities in space form: results and open problems

时间:2019-10-15

TitleMinkowski type inequalities in space form: results and open problems
Speaker:Guan Pengfei  教授   (麦吉尔大学)
Time2019年10月18日             下午  16:00-17:00
Room东区管理科研楼  澳门新葡新京1418室

AbstractThe Minkowski inequality states that, for a convex body $/Omega/subset /mathbb R^{n+1}$, $/int_{/partial /Omega}H d/sigma /ge C_n (/int_{/partial /Omega} d/sigma)^{/frac{n-1}{n}}$ for some dimensional constant $C_n>0$, the equality holds if and only if $/Omega$ is a round ball. This inequality has been extended for starshaped domains (Guan-Li) and for area outer minimizing domains (Huisken). In this talk, the focus is this type of inequality in space form: hyperbolic space $/mathbb H^{n+1}$ and elliptic space $/mathbb S^{n+1}$. We will discuss some recent results and challenging open problems.


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