Bernstein-type and sheeting-type results for stable minimal hypersurfaces
Geometry and analysis of special structures on manifolds November 18, 2024 - November 22, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
We consider properly immersed two-sided stable minimal hypersurfaces of dimension n. We illustrate the validity of curvature estimates for n \leq 6 (and associated Bernstein-type properties with an extrinsic area growth assumption). For n \geq 7 we illustrate sheeting results around "flat points". The proof relies on PDE analysis. The results extend respectively the analogous Schoen-Simon-Yau estimates (obtained for n \leq 5) and the Schoen-Simon sheeting theorem (valid for embeddings).