Organized by
Department of Mathematics
Joint Research Institute for Applied Mathematics

The Extremal Kahler Metrics on Toric Manifolds

Professor An-min Li

Academician of Chinese Academy of Sciences
Professor of Sichuan University


Date: 14 February 2012 (Tuesday)

11:30am - 12:30pm (Preceded by Reception at 11:00am)

SCT909, Cha Chi-ming Science Tower,
Ho Sin Hang Campus,
Hong Kong Baptist University


We study the prescribed scaler curvature problem on toric manifolds. We will show that the uniform stability introduced by Donaldson is a necessary condition for existing a smooth solution for any dimension n. For the case n = 2 we prove that this condition is also sufficient. More precisely, we prove the following theorem:

Theorem Let M be a compact toric surface and Delta be its Delzant polytope. Let K in Cinfty (bar{Delta}) be an edge-nonvanishing function. If (M, K) is uniformly stable, then there is a smooth T2-invariant metric on M that solves the Abreu equation.

This talk is based on the joint works with Bo-hui Chen and Li Sheng




All are welcome