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arXiv · 2402.17330

Geometric criteria for the existence of capillary surfaces in tubes

Giorgio Saracco
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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 $\Omega$.

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Giorgio Saracco. 2024-02-27. Geometric criteria for the existence of capillary surfaces in tubes. https://doi.org/10.1016/j.exmath.2024.125547

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