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.
back to the seminar homepage