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：王一 教授 （Johns Hopkins University）
题 目：Rigidity of local minimizers of the σk functional
时 间：2022.07.13（星期三）上午09:00-10:00
地 点：Zoom：684 9121 0020 Code：564063
摘 要：In this talk, I will present a result on the rigidity of local minimizers of the functional $\int \sigma_2+ \oint H_2$ among all conformally flat metrics in the Euclidean (n + 1)-ball. We prove the metric is flat up to a conformal transformation in some (noncritical) dimensions. We also prove the analogous result in the critical dimension n + 1 = 4. The main method is Frank-Lieb’s rearrangement-free argument. If minimizers exist, this implies a fully nonlinear sharp Sobolev trace inequality. I will also discuss a nonsharp Sobolev trace inequality. This is joint work with Jeffrey Case.