Geometric Analysis and Topology Seminar

---

Boundary regularity of capillary surfaces

Speaker: Benjy Firester, MIT

Location: Warren Weaver Hall 512

Date: Friday, December 5, 2025, 11 a.m.

Synopsis:

We discuss new development on the boundary regularity of capillary hypersurfaces. Capillary surfaces are hypersurfaces in Riemannian manifolds with boundary with prescribed mean curvature and contact angle at the boundary; of particular interest are minimal examples. We construct minimal capillary cones by solving a non-linear free boundary equation giving examples in all dimensions which exhibit various regularity behaviors depending on the symmetry group. Our results further indicate the optimal regularity theory of related free boundary PDEs.