主讲人：方浩 教授（美国IOWA大学）

时  间：6月16日（周四）14：50-15：50

地  点：数学科学学院 210 教室

备  注：摘要：In previous works with Lai and Ma, we discussed a type of fully non-linear PDEs on a Kaehler manifold and gave a necessary and sufficient cone condition for the existence of unique smooth solution. In this recent joint work in progress with Lai, we gave family of geometric flows approaching the above-mentioned solution, generalizing the previous result. We also discuss the situation when the necessary and sufficient condition fails and the initial data lies on the boundary of the admissible cone. For Kaehler manifolds satisfying the Calabi-Ansatz, we prove the the existence of continuous solutions with blown-up $C^2$ norm for this case, which can be viewed as an analogue of corresponding results on the Monge-Ampere equation and the Kaehler-Ricci flow. This approach gives another geometric method to detect and blow down the exceptional divisor in algebraic geometry.