Mathematical Sciences: Heat Flow on Riemannian Manifolds

利用Ricci流发展方程的技巧，研究了某些完备的具有正对分曲率的非紧Kaehler流形的结构，具有正曲率算子的紧致黎曼流形的光滑结构，以及某些紧致Kaehler流形上Kaehler-Einstein度量的存在性.这项研究涵盖了现代微分几何中的几个主题。演化方程的几何化在数学物理、全球变化、人口研究和生物科学的许多领域都得到了实现。预计调查员将积极参与研究生的培训。

Using the technique of the Ricci flow evolution equation, the investigator will study the structure of certain classes of complete non-compact Kaehler manifolds with positive bisectional curvature, the smooth structure of compact Riemannian manifolds with positive curvature operator and the existence of Kaehler- Einstein metrics on certain compact Kaehler manifolds. The research covers several topics in modern differential geometry. The geometry of evolution equations is realized in many fields of mathematical physics, areas relating to global change, population studies and the biological sciences. It is expected that the investigator will be active in the training of graduate students.