Calculus of Variations and Geometric Measure Theory

PDE analysis on stable minimal hypersurfaces: curvature estimates and sheeting

Costante Bellettini

created by scharrer on 28 Jun 2025

16 jul 2025 -- 13:00   [open in google calendar]

Agenda: Get-together (30 min), presentation Costante Bellettini (60 min), questions and discussions (30 min).

Registration required for new participants. Please go to our seminar website (allow one work day for processing).

Abstract.

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 Schoen-Simon-Yau estimates (obtained for $n \leq 5$) and the Schoen-Simon sheeting theorem (valid for embeddings).