Mathematical Sciences: Geometry and Analysis on Kahler Manifolds

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9504925 Cao The proposal lies in complex geometry and differential equations, and deals specifically with the Ricci flow - otherwise known as the parabolic Einstein equation, which is a geometric evolution equation - on Kahler manifolds. The main goal is to understand the asymptotic behavior of solutions to the Ricci flow on a compact Kahler manifold of positive holomorphic bisectional curvature. Geometric evolution equations arise in nature. And although the proposed research deals with somewhat technical aspects of a specific geometric evolution equation, it is possible that it will lead to important techniques applicable to a broader class of evolution equations.