题目：A Class of Equations from the Conformal Geometry
报告人：徐露 教授 （湖南大学）
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 .
ID：298 167 877
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