Special Session 91: Geometric evolution problems

Rigidity of minimal and CMC hypersurfaces.
Han Hong
Beijing Jiaotong University
Peoples Rep of China
Co-Author(s):    
Abstract:
This talk will present a broad overview of rigidity results for stable and finite-index minimal (or constant mean curvature) surfaces. We will survey key milestones in the field, including the stable Bernstein problem for minimal hypersurfaces, its capillary surface analogue, do Carmo`s problem for non-minimal CMC hypersurfaces, and rigidity theorems for stable minimal hypersurfaces in general Riemannian manifolds. The presentation will focus on the statements of these results and their geometric significance, without delving into the technical details of the proofs.