Floating bodies in neutral equilibrium
Robert Finn and Mattie Sloss
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Submission date: 06. Nov. 2007 (revised version: November 2007)
published in: Journal of mathematical fluid mechanics, 11 (2009) 3, p. 459-463
DOI number (of the published article): 10.1007/s00021-008-0269-y
MSC-Numbers: 76B45, 52A15
Keywords and phrases: capillarity, contact angle, floating criteria, convex bodies, neutral equilibrium
In the paper just preceding in this issue, Finn proved that if the contact angle γ of a convex body B with a given liquid is π/2, and if B can be made to float in “neutral equilibrium” in the liquid in any orientation, then B is a metric ball. The present work extends that result, with an independent proof, to any contact angle in the range 0 < γ < π. Our result is equivalent to the general geometric theorem that if for every orientation of a plane, it can be translated to meet a given strictly convex body B in a fixed angle γ within the above range, then B is a metric ball.