报告名称：The -curvature equation on a compact manifold with boundary

报告专家：韦韡

专家所在单位：南京大学

报告时间：2023年8月31日周四15：00-16：00

报告地点: 腾讯会议：474-437-376

专家简介： 韦韡，现南京大学研究员，博士毕业于中国科学技术大学，上海数学中心博士后。曾获得博士后创新人才计划。在 Adv.Math, J.Funct. Anal., Calc. Var.等杂志发表过多篇高质量论文。

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.