Regularity of capillary minimal surfaces

Abstract: A capillary surface is a hypersurface meeting some container at a prescribed angle, like the surface of water in a cup. In this talk I describe some recent results concerning the boundary regularity of capillary surfaces which either minimize or are critical for their relevant energy. The first result (joint with O. Chodosh and C. Li) is an improved dimension bound for the boundary singular set of energy-minimizers, exploiting the connection between capillary minimal surfaces and the one-phase Bernoulli problem. The second (joint with L. de Masi, C. Gasparetto, and C. Li) is an Allard-type regularity theorem for energy-critical capillary surfaces near capillary half-planes, which implies regularity at generic boundary points of density $< 1$.

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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