Department of Mathematics
Sponsored by Hung Hin Shiu Charitable Foundation

On Fourth Order PDEs in Affine Differential Geometry and Complex Differential Geometry

Professor Anmin Li

Sichuan University, China
Academician of Chinese Academy of Sciences


Date: 13 February 2014 (Thursday)

4:00 pm - 5:00 pm (Preceded by Reception at 3:30 pm)


1/F Shiu Pong Hall,
Hong Kong Baptist University



Consider the following equation

sum_{i,j=1}^n U^{ij} w_{ij} = - L, w =[det((partial^2 u)/(partial xi_i partial xi_j))]^a,

where L is some given C^infty function, u(xi) is a smooth and strictly convex function defined in a convex domain in R^n, (U^{ij}) denotes the cofactor matrix of the Hessian matrix (partial^2 u)/(partial xi_i partial xi_j) and a <> 0 is a constant. When a = -(n+1)/(n+2) and L=0, the above equation is the equation for affine maximal hypersurfaces. When a = -1 it is called the Abreu equation, which appears in the study of the differential geometry of toric varieties, where L is the scalar curvature of the Kahler metric. In this talk, we will discuss some recent development on the study of the relevant differential equations in the differential geometry.


All are welcome