The Kahler-Ricci flow and stability


Duong Hong Phong

Columbia University

Harvard University

Thursday, October 11, 2007


Talk at 4:30 p.m. in Science Center D

Tea at 4:00 p.m. in the Math Lounge


Abstract:   The Kahler-Ricci flow is a parabolic flow of metrics, whose fixed points are Kahler-Einstein metrics. According to a well- known conjecture of Yau, the existence of such metrics, and hence the convergence of the flow, should be equivalent to the stability of the underlying manifold in the sense of geometric invariant theory. We discuss recent progresses in this direction, including conditions for the convergence of the flow in terms of orbits of almost-complex structure under the diffeomorphism group, and lower bounds for the $\bar\partial$-operator on vector fields.


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Posted: September 28, 2007    URL: