偏微分方程研讨班：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：陈学长 教授（南京大学）   

题  目：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds

时  间：2023.11.14（星期二）上午10:00-11:00

地  点：思源楼S813

摘 要：On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a conformal metric having a positive sigma-2 curvature and a non-negative boundary mean curvature, which is necessary as shown by counter-examples. Two obstructions to the existence result are well-known to experts in this field: One is local C2 estimates near generic boundary; the other is to build the blow-up analysis based on local estimates. In this talk, we are only enough to outline  the proof of latter part, i.e. blow-up analysis, assuming the local C2 estimates. This is joint work with Wei Wei.