Abstract
It is shown by making use of an invariance property of a symmetrization process of Steiner that the free surface of a liquid bridge or a soap film which connects the edges of flat coaxial parallel plates is generated by rotation of a curve representable as r = r(z), which is stable towards small axisymmetric disturbances and is also stable towards small non-axisymmetric disturbances when both types of disturbance leave invariant the end circles and the volume enclosed by the free surface and end plates. A corresponding result is also proven for liquid bridges between convex solids in the zero contact angle case.
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