PDE analysis on stable minimal hypersurfaces: curvature estimates and sheeting

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).

analysis of PDEsdifferential geometry

Audience: researchers in the topic

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NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

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