报告人：沈伟明博士

北京国际数学研究中心

报告题目：On Negativity of Ricci Curvatures of Complete Conformal Metrics

报告时间：2017年11月10日下午15:30

报告地点：海韵实验楼105

摘要：A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures. In this talk, I will disscuss whether these metrics have negative Ricci curvatures. We will provide a general construction of domains in compact manifolds and demonstrate that the negativity of Ricci curvatures does not hold if the boundary is close to certain sets of low dimension. The expansion of the Green's function and the positive mass theorem play essential roles in certain cases. On the other hand, we prove that these metrics indeed have negative Ricci curvatures in bounded convex domains in the Euclidean space.

报告人简介：沈伟明，2016年于北京大学获得博士学位，现北京国际数学研究中心博士后。主要从事几何分析领域研究。最近在奇异共形椭圆方程及几何应用方向做出了突出工作。

学院联系人：、杨波副教授

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