Vertex theorems for capillary drops on support planes

Details Vertex theorems for capillary drops on support planes Vertex theorems for capillary drops on support planes

1997-07-07

arxiv.org/abs/math/9707217v1

Mathematics

Differential Geometry

Scientific paper

We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or equal to three, then the free surface must be a portion of a sphere. These results extend the classical theorem of H. Hopf on constant mean curvature immersions of the sphere. The conclusion of sphericity cannot be extended to more than three vertices, as we show by examples.

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