Differential Geometry Seminar
We study a conformal isoperimetric inequality proved by Hang-Wang-Yan 09. The maximizer of the isoperimetric quotient is given by an integral equation. We proved that a solution to HWY's integral equation is equivalent to solve a Serrin type overdetermined equation. We proposed an eigenvalue problem resemble the Steklov eigenvalue problem which is related to HWY's inequality.