Improved regularity for minimizing capillary hypersurfaces

Abstract

We give improved estimates for the size of the singular set of minimizing capillary hypersurfaces: the singular set is always of codimension at least $4$, and this estimate improves if the capillary angle is close to $0$, $\frac{\ddot{I}}{€}2$, or $\ddot{I}€$. For capillary angles that are close to $0$ or $\ddot{I}€$, our analysis is based on a rigorous connection between the capillary problem and the one-phase Bernoulli problem.