-Title: Rigidity theorems of hypersurfaces with free boundary in a wedge in a space form

- Speaker:Prof. Juncheol Pyo (Pusan National University)

- Abstract: A geodesic sphere in a space form is characterized in various ways. Among all hypersurfaces of a given volume bounding a domain in a space form, a geodesic sphere has the least area, that is, it is the boundary of an isoperimetric domain in a space form. In this talk, we present some rigidity results about compact hyper surfaces with free boundary in a wedge in a space form. First, we prove that every compact immersed stable constant mean curvature hypersurface with free boundary in a wedge is part of a geodesic sphere centered at a point of the edge of the wedge. Second, we show that the same rigidity result holds for a compact embedded constant higher order mean curvature hypersurface with free boundary in a wedge. Finally, we extend this result to a compact immersed hypersurface with free boundary in a wedge that has the additional property that the ratio of two higher order mean curvatures is constant.

- Place: Math Science bldg. Room 404

- Date: 5 p.m.- on Wednesday, June 3, 2015

Organized by Jae Choon Cha, Kang-Tae Kim, and Yong-Geun Oh