A Heintze-Karcher inequality with free boundaries and applications to capillarity theory
Matias G. Delgadino, Daniel Weser
TL;DR
This paper extends the Heintze-Karcher inequality to mean convex hypersurfaces with free boundaries on curved substrates, providing new insights into the shape of droplets in capillarity theory.
Contribution
It introduces a novel form of the Heintze-Karcher inequality applicable to free boundary hypersurfaces on curved substrates, advancing the mathematical understanding of capillarity phenomena.
Findings
Derived a new Heintze-Karcher inequality for free boundary hypersurfaces
Characterized droplet shapes within curved containers in capillarity regime
Provided mathematical tools for analyzing capillarity problems with curved boundaries
Abstract
In this paper we analyze the shape of a droplet inside a smooth container. To characterize their shape in the capillarity regime, we obtain a new form of the Heintze-Karcher inequality for mean convex hypersurfaces with boundary lying on curved substrates.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical Dynamics and Fractals · Textile materials and evaluations