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On a singular behavior of capillary surfaces

Authors:	Email author" target="_blank">Robert?Finn Email author Darren?Lee

Institution:	(1) Mathematics Department, Stanford University, CA 94305-2125 Stanford, USA;(2) Courant Institute of Mathematical Sciences, 251 Mercer Street, NY 10012-1110 New York, USA

Abstract:	Mario Miranda raised the question, whether a capillary tube of section ${\cal D}_{0}$ in an infinite bath under a uniform downward gravity field always raises liquid higher over its section than does a tube of the same material and section ${\cal D}_1 \supset \supset {\cal D}_0$ . Finn and Kosmodemyanskii, Jr. recently gave conditions under which a negative answer is obtained for all gravity small enough; they gave also an example in which ${\cal D}_0$ is a disk and in which the answer changes in a discontinuous way, for fixed ${\cal D}_1$ and differentiable change of $\partial {\cal D}_0$ . In the present work we characterize the most general convex ${\cal D}_1$ for which such a discontinuous change can occur.Received: 3 September 2002, Accepted: 23 January 2003, Published online: 1 July 2003Mathematics Subject Classification: 76B45, S3A10, 49Q10

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