Abstract

We describe the construction of new exotic containers in a gravitational field. These are containers which, for certain volumes of fluid, possess a continuum of noncongruent equilibrium configurations. Unlike the constructions of Gulliver and Hildebrandt (1986) and Concus and Finn (1991), our containers need not be rotationally symmetric. One of their features is that the equilibria seem likely to be local minimizers of energy, in contrast to earlier constructions where the equilibria were always unstable.

Keywords

capillarity, prescribed mean curvature, exotic containers

Mathematical Subject Classification

Primary: 53A10

Secondary: 49Q10, 35F10

Authors