学术报告

A Class of Equations from the Conformal Geometry 

阅读次数:49

题目:A Class of Equations from the Conformal Geometry 
报告人:徐露 教授 (湖南大学) 
地点:腾讯会议室
时间:2020年5月26日 09:00-10:00
摘要:We solve the Gursky-Streets equations with uniform C^1,1 estimates for  . An important new ingredient is to show the concavity of the operator which holds for all  . Our proof of the concavity heavily relies on Garding's theory of hyperbolic polynomials and results from the theory of real roots for (interlacing) polynomials. Together with this concavity, we are able to solve the equation with the uniform C^1,1 a priori estimates for all the cases  . Moreover, we establish the uniqueness of the solution to the degenerate equations for the first time.
As an application, we prove that if   and   is conformally flat, any solution solution of  -Yamabe problem is conformal diffeomorphic to the round sphere  . 
腾讯会议室
https://meeting.tencent.com/s/N8qY3IfWQz6y
ID:298 167 877

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