arXiv:2210.16376 Abstract | arXiv Analytics

arXiv:2210.16376 [math.AP]Abstract References Reviews Resources

A Heintze--Karcher inequality with free boundaries and applications to capillarity theory

Published 2022-10-28Version 1

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 hypersufaces with boundary lying on curved substrates.

Comments: 31 pages, 3 figures, comments welcome!

Categories: math.AP, math-ph, math.DG, math.MP

Keywords: heintze-karcher inequality, free boundaries, capillarity theory, applications, mean convex hypersufaces

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