November 1, 2006

Xiuxiong Chen (Madison):   The almost C^\infinity regularity of homogeneous MA equation (arising from Kähler geometry) and its application

Abstract:

Joint with G. Tian, we prove that for generic boundary data, the solution to the disc version geodesic equation is almost everywhere smooth. In particular, the K energy (Largangian functional for cscK metric equation) is a subhamonic function when restricted to this disc family. As an application, this proves that the uniqueness of extremal Kähler metrics. More recently (last fall), I proved that the sharp lower bound of the Calabi energy (L^2 norm of scalar curvature) hold in any Kähler class.

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