报告人：周恒宇（重庆大学）

报告题目：Prescribed meancurvature hypersurfaces in conformally product manifolds

时间：2022年9月15日 14:00-15:00

地点：腾讯会议号：815 811 132，无需密码

报告摘要：

 In this paper we characterize the  L^1 convergence of C^2 bounded functions such that their graphs have uniformly bounded mean curvature. As an application with Gerhardt's approximate process, we established the existence of closed or C^｛3，alpha｝ compact  prescribed mean curvature (PMC) hypersurfaces in conformally product manifolds with its mean curvature equal to a C^｛1，alpha｝ function under a natural barrier condition. Moreover, these hypersurfaces are homeomorphic to the underlying n-dimensional Riemannian manifold for 2=<n=<7. In addition, if a quasi-decreasing condition of PMC functions is satisfied, such PMC hypersurfaces are C^1 graphs.