Rigidity of Critical Points of Hydrophobic Capillary Functionals

Explore the mathematical rigidity properties of critical points in hydrophobic capillary functionals through this 38-minute conference lecture. Examine the proof of rigidity among sets of finite perimeter for volume-preserving critical points of capillary energy in half-space configurations, specifically when prescribed interior contact angles range between 90° and 120°. Learn how this rigidity theorem requires no structural or regularity assumptions on finite perimeter sets and discover its extension to the complete hydrophobic regime covering interior contact angles from 90° to 180° under the condition that the tangential part of the capillary boundary is H^n-null. Investigate the anisotropic counterpart of this theorem when lower density bounds are assumed, based on collaborative research with R. Neumayer and R. Resende presented as part of the Thematic Programme on Free Boundary Problems at the Erwin Schrödinger International Institute for Mathematics and Physics.