Capillary minimizing hypersurfaces and the one-phase Bernoulli problem

Speaker: Chao Li

Location: Warren Weaver Hall 1302

Date: Feb. 6, 2026, 1 p.m.

Capillary surfaces are the mathematical model of fluid interfaces and arise naturally as (constrained) minimizers of the Gauss free energy. The one-phase Bernoulli problem is a mathematical formulation of a typical free-boundary phenomenon. These two problems both have a variational characterization. The existence, regularity and the geometry of their solutions have been extensively studied separately.

In this talk, I will discuss recent progress on the connection of these two problems, and in particular, why the one-phase Bernoulli problem is a linearization of the capillary problem. I will also explain how one may use this connection to derive new regularity results on the capillary problem.