Frankel property and Maximum Principle at Infinity for complete minimal hypersurfaces
数学专题报告
报告题目(Title)：Frankel property and Maximum Principle at Infinity for complete minimal hypersurfaces
报告人(Speaker)：Jose M. Espinar (Universidad de Cadiz, Spain)
地点(Place)：ZoomID: 941 3577 6085 密码: 794539
时间(Time)：2023 年 10月 26日16：00—17：00
邀请人(Inviter)： 熊金钢
报告摘要
We extend Mazet's Maximum Principle at infinity for parabolic, two-sided, properly embedded minimal hypersurfaces, up to ambient dimension seven. Parabolicity is a necessary condition in dimension n≥ 4, even in Euclidean space, as the example of the higher-dimensional catenoid shows. Next, inspired by the Tubular Neighborhood Theorem of Meeks-Rosenberg in Euclidean three-space we focus on the existence of an embedded ϵ−tube when the ambient manifold M has non-negative Ricci curvature. These results will allow us to establish Frankel-type properties and to extend the Anderson-Rodriguez Splitting Theorem under the existence of an area-minimizing mod(2) hypersurfaceΣin these manifolds
M (up to dimension seven), the universal covering space of M is isometric to Σ×R with the product metric.
* This PDE seminar is co-organized with Tianling Jin at The Hong Kong University of Science and Technology. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
