中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

时  间：2022.05.18（星期三）

地  点：腾讯会议：372-1337-1800，密码：0817

n  下午2：00-3：00

报告人：叶剑 （南京大学）

题  目：Homogeneous Mobius equation on Riemannian manifold

摘 要：In this talk, we discuss homogeneous Mobius equation on Riemannian manifold. We give a necessary and sufficient condition to the existence of non-trivial smooth solution to homogeneous Mobius equation on closed manifold.  Then we introduce several generalizations of this result. This work is jointed with Prof. Xingwang Xu.

n  下午3：00-4：00

报告人：王邵东（上海交通大学）

题 目：On Yamabe-type equations on manifolds with boundary

摘 要：In this talk, I will present some recent results on the existence and compactness of Yamabe-type equations on manifolds with boundary. The Yamabe problem plays an important role in the study of conformal geometry and partial differential equations. Geometrically, it establishes conformal metrics on Riemannian manifolds with constant curvatures. From a PDE point of view, it corresponds to differential equations with critical nonlinearities. I will discuss recent developments in the field as well as some possible projects of personal interest. The talk is based on joint works with Sergio Almaraz, Olivaine Queiroz and Jerome Vetois.