汇报标题 (Title)： 带边紧流形上$\sigma_{2}$曲率方程（The $\sigma_{2}$-curvature equation on a compact manifold with boundary）
汇报人 (Speaker)： 韦韡 钻研院（漯河大学）
汇报功夫 (Time)：2023年11月2日 (周四) 10:00-12:00
汇报地址 (Place)： 腾讯会议728-720-963
约请人(Inviter)：高正焕
主办部门：理学院数学系
汇报提要：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.
