报告题目 (Title)： 带边紧流形上$\sigma_{2}$曲率方程（The $\sigma_{2}$-curvature equation on a compact manifold with boundary）
报告人 (Speaker)： 韦韡 研究员（南京大学）
报告时间 (Time)：2023年11月2日 (周四) 10:00-12:00
报告地点 (Place)： 腾讯会议728-720-963
邀请人(Inviter)：高正焕
报告摘要：We first establish local $C^2$ estimates of solutions to the $\sigma_2$-curvature equation with nonlinear Neumann boundary condition. Then, under assumption that the background metric has nonnegative mean curvature on totally non-umbilic boundary, for dimensions three and four we prove the existence of a conformal metric with a prescribed positive $\sigma_2$-curvature function and a prescribed nonnegative boundary mean curvature function. The local estimates play an important role in blow up analysis in the latter existence result.