Extremal Metrics for the Spectrum of the Laplacian on Closed Manifolds -

Extremal Metrics for the Spectrum of the Laplacian on Closed Manifolds

Time: 2018-07-04 Published By: He Liu

Speaker(s): Yannick Sire (Johns Hopkins University)

Time: 15:00-16:00 July 11, 2018

Venue: Room 77201, Jingchunyuan 78, BICMR

I will report on a program in proving existence and isoperimetric inequalities for extremal metrics in conformal classes for the eigenvalues of the Laplace-Beltrami on surfaces, with a particular emphasis on the case of the 2-sphere. then I will move on to higher dimensional versions where the laplacian is replaced by the conformal laplacian. In this case several striking phenomena occur. I will mention several open problems and directions of research, involving in particular complex geometry.