Vol. 224, No. 2, 2006

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ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
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Ryan Hynd & John McCuan

Abstract

The existence of toroidal rotating drops was observed experimentally by Plateau in 1841. In 1983 Gulliver rigorously showed that toroidal solutions of the governing equilibrium equations do indeed exist. In this short note, we settle two questions posed by Gulliver concerning the existence of additional toroidal solutions. We use a general assertion concerning rotationally symmetric surfaces whose meridian curves have inclination angle given as a function of distance from the axis along with explicit estimates for rotating drops.

Keywords

rotating drops, mean curvature, Plateau, Delaunay

Mathematical Subject Classification

Primary: 49J05, 76B45

Authors
Ryan Hynd
 
John McCuan
School of Mathematics
Georgia Institute of Technology
686 Cherry Street
Atlanta, GA 30332-0160
United States