Calculus of Variations and Geometric Measure Theory

G. Saracco

Geometric criteria for the existence of capillary surfaces in tubes

created by saracco on 27 Feb 2024
modified on 04 Mar 2024


Accepted Paper

Inserted: 27 feb 2024
Last Updated: 4 mar 2024

Journal: Expo. Math.
Volume: 42
Number: 3
Pages: 125547
Year: 2024
Doi: 10.1016/j.exmath.2024.125547

ArXiv: 2402.17330 PDF


We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes $\Omega\times \mathbb{R}$ in a gravity free environment, in the case of physical interest, that is, for bounded, open, and simply connected $\Omega \subset \mathbb{R}^2$. These criteria rely on suitable weak one-sided bounds on the curvature of the boundary of the cross-section $\Omega$.

Keywords: Cheeger sets, Curvature, capillary surfaces, sets of positive reach