UW AGD Seminar: Robin Neumayer

The capillary energy functional models the equilibrium shape of a liquid drop meeting a substrate at a prescribed interior contact angle. We will discuss a rigidity theorem for volume-preserving critical points of the capillary energy in the half-space: among all sets of finite perimeter, every such critical configuration corresponding to a prescribed contact angle between $90^{\circ}$ and $120^{\circ}$ must be a finite union of spheres and spherical caps with the correct contact angle. Assuming that the tangential part of the capillary boundary is $\mathcal{H}^n$-null, this rigidity extends to the full hydrophobic range of contact angles between $90^{\circ}$ and $180^{\circ}$. We will also present an anisotropic counterpart, establishing rigidity under suitable lower density assumptions.