On the isoperimetric ratio over scalar-flat conformal classes

：金天灵助理教授
：2020-01-02 14:00
：实验楼105

       Speaker： Dr. Tianling Jin

                        The Hong Kong University of Science Technology

Title:    On the isoperimetric ratio over scalar-flat conformal classes

       Time：02 Jan 2020, 14:00

Location：实验楼105

Abstract:   Let (M,g) be a smooth compact Riemannian manifold of dimension n with smooth boundary. Suppose that (M,g) admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric ratio over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality on Euclidean space, consequently is achieved, if either (i) n>=9 the boundary has a nonumbilic point; or (ii) n>=7, the boundary is umbilic the Weyl tensor does not vanish at some boundary point. A crucial ingredient in the proof is the expansion of solutions to the conformal Laplacian equation with blowing up Dirichlet boundary conditions.

 Speaker  Introduction：金天灵，香港科技大学数学系助理教授。2006年本科毕业于中国科学技术大学，2012年博士毕业于美国Rutgers大学，曾在Chicago大学从事博士后研究。他的研究方向是非线性偏微分方程和几何分析。在包括Math. Ann., JEMS, Adv. Math.,TAMS, ARMA, Ann. IHP，CPDE, CVPDE, IMRN等的国际著名期刊发表SCI论文20余篇。

 

 

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