Mathematical Sciences: Geometry and Analysis on Kahler Manifolds

小行星9504925 该提案在于复杂的几何和微分方程，并专门处理里奇流-也被称为抛物爱因斯坦方程，这是一个几何演化方程-在卡勒流形。主要目的是了解正全纯双截曲率紧致Kahler流形上Ricci流解的渐近行为。 几何演化方程起源于自然界。虽然所提出的研究涉及特定几何演化方程的一些技术方面，但它可能会导致适用于更广泛类别的演化方程的重要技术。

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.