PDE Seminar Abstracts

Gap theorems involving second fundamental form: from closed surfaces to open surfaces

Changwei Xiong
Australian National University
Mon 20th Mar 2017, 2-3pm, Carslaw Room 829 (AGR)


In this talk I will start with a classical gap theorem due to Chern, do Carmo and Kobayashi, and Lawson, independently, which characterises the equators and Clifford tori among closed minimal hypersurfaces in a standard sphere. Then I will move from closed minimal submanifolds in a sphere to open minimal submanifolds with free boundary in a Euclidean ball, and along the way review some open problems. Finally I shall present gap theorems in the open minimal surfaces with free boundary setting, which consist of the Euclidean result due to Ambrozio and Nunes, and the hyperbolic and spherical result due to Haizhong Li and myself.