

Preprint 73/2009
Floating criteria in three dimensions
Robert Finn and Thomas Vogel
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Submission date: 09. Dec. 2009
published in: Analysis, 29 (2009) 4, p. 387-402
DOI number (of the published article): 10.1524/anly.2009.0931
Bibtex
MSC-Numbers: 76B45, 49Q10, 53A10
Keywords and phrases: capillarity, surface tension, floating bodies
Abstract:
We extend to objects of general convex form an earlier criterion given by Finn for
ensuring a local energy minimum corresponding to floating of a heavy horizontal cylinder on a
liquid surface. We obtain a formal analogue of Finn’s criterion, and additionally a condition on
interfacial surface energies under which an object of given shape with density exceeding that of the
liquid must float if it is scaled to be sufficiently small. In analogy with Finn’s earlier work, we show
also in the more physical case presently considered that if a body is lowered rigidly from a position
above the undisturbed liquid surface to a position below the surface, the liquid configuration must
change during the motion in a discontinuous way.