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 proofs rely on intrinsic (nonlinear) PDE analysis. The two main results extend respectively the analogous Schoen-Simon-Yau estimates (obtained for n \leq 5) and the Schoen-Simon sheeting theorem (valid for embeddings).

Biography: Costante Bellettini is currently a Professor at University College London. He obtained his PhD in 2011 at ETH Zurich, under the supervision of Tristan Riviere. His research is in geometric analysis, in particular minimal surfaces.

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