Abstract

In this talk I will present an Allard-type regularity theorem for minimal surfaces meeting the boundary of a container with a prescribed angle, obtained in collaboration with N. Edelen, C. Gasparetto and C. Li: if a stationary surface for a capillarity functional is close to a half-plane in a weak measure-theoretic sense, then it is a $C^{1,\alpha}$-graph over the half-plane with uniform estimates.
The proof relies on a "boundary length" control (a fact with its own interest) and viscosity techniques.