Geometry and Topology Seminar

Series: Geometry and Topology Seminar Series

PDE analysis on stable minimal hypersurfaces: curvature estimates and sheeting

Costante Bellettini, Department of Mathematics, University College London,

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).

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