Geometric Analysis and Topology Seminar

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PDE analysis on stable minimal hypersurfaces: curvature estimates and sheeting

Speaker: Costante Bellettini, University College London

Location: Warren Weaver Hall 512

Date: Friday, April 26, 2024, 11 a.m.

Synopsis:

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). 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).