Department of Mathematics,
University of California San Diego
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Math 258: Seminar in Differential Geometry
Prof. Nick Edelen
University of Notre Dame
Improved regularity for minimizing capillary hypersurfaces
Abstract:
Capillary surfaces model the geometry of liquids meeting a container at an angle, and arise naturally as (constrained) minimizers of the Gauss free energy. 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 in the surface, and this estimate improves if the capillary angle is close to $0$, $\pi/2$, or $\pi$. For capillary angles that are close to $0$ or $\pi$, our analysis is based on a rigorous connection between the capillary problem and the one-phase Bernoulli problem. This is joint work with Otis Chodosh and Chao Li.
Host: Luca Spolaor
May 22, 2025
1:00 PM
APM B412
Research Areas
Geometric Analysis****************************
