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
Abstract:
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
Download: