Description:

Title: Improved regularity for minimizing capillary hypersurfaces

Abstract: Capillary surfaces model the geometry of liquids meeting a container at an angle, and arise naturally as (constrained) minimizers of the Gauss free energy.  We give improved estimates for the size of the singular set of minimizing capillary hypersurfaces: the singular set is always of codimension at least 4 in the surface, and this estimate improves if the capillary angle is close to $0$, $\pi/2$, or $\pi$. For capillary angles that are close to $0$ or $\pi$, our analysis is based on a rigorous connection between the capillary problem and the one-phase Bernoulli problem.  This is joint work with Otis Chodosh and Chao Li.