On toroidal rotating drops

Ryan Hynd and John McCuan

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Submission date: 10. Feb. 2006
Pages: 12
published in: Pacific journal of mathematics, 224 (2006) 2, p. 279-289 
Bibtex
Keywords and phrases: rotating drops, mean curvature, Plateau, Delaunay
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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.