Free boundary hypersurfaces in the unit ball
speaker: Guofang Wang (University of Freiburg)abstract: In this talk I will first introduce a new Minkowski formula for free boundary hypersurfaces in the unit ball. Using this formula we prove that a stable free boundary CMC hypersurface is a spherical cap, which completes the stable result starting from the work of Ros-Vergasta. A similar proof works also for stable capillary hypersurfaces in a ball. Using this Minkowski formula we also establish a Heintze-Karcher-Ros type inequality for free boundary hypersurfaces, from which an Alexandrov type theorem follows. Moreover, by this Minkowski formula we introduce a Guan-Li type mean curvature flow for free boundary hypersurfaces, which has applications in establishing geometric inequalities for free boundary hypersurfaces. This is a joint work with Chao Xia (Xiamen University)
timetable:
Thu 7 Jun, 16:00 - 17:00, Aula Dini
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