MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

On toroidal rotating drops

Ryan Hynd and John McCuan


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.

rotating drops, mean curvature, Plateau, Delaunay

Related publications

2006 Repository Open Access
Ryan Hynd and John McCuan

On toroidal rotating drops

In: Pacific journal of mathematics, 224 (2006) 2, pp. 279-289