Prescribing σ2 curvature and boundary mean curvature problem

讲座时间 Datetime: 2023年7月5日，星期三， 14:00-15:30

地点 Venue: 海琴二号A457

报告人 Speaker: 陈学长 教授

单位 Affiliation: 南京大学

主持人Host：魏国栋 副教授

报告摘要 Abstract:

On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，under some natural non-negativity assumptions on curvatures of the background metric, we establish that there exists a conformal metric with a prescribed positive σ2 curvature and a prescribed non-negative boundary mean curvature function. One among key ingredients is to establish the a priori C2 estimate of solutions to the σ2 curvature with nonlinear Neumann boundary condition. However, such an estimate remains open in the non-umbilic boundary before ours.  For the existence part, it is important to build blow-up analysis. In this talk, we mostly focus on local C2 estimate. This is joint work with Wei Wei.

报告人简介：

陈学长，南京大学数学系教授。陈教授的研究方向是几何分析与偏微分方程，现在主要关注的是共形几何中的预定曲率问题及相关曲率流、紧致带边流形上的几何不等式以及几何刚性现象等。文章发表在Invent. Math, Adv. Math等国际知名数学期刊上。