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MiS Preprint

Vertex theorems for capillary drops on support planes

Robert Finn and John McCuan


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.

MSC Codes:
76B45, 53A10, 53C42, 49Q10
capillarity, mean curvature, liquid drops, wedges, polyhedral angles

Related publications

2000 Repository Open Access
Robert Finn and John McCuan

Vertex theorems for capillary drops on support planes

In: Mathematische Nachrichten, 209 (2000), pp. 115-135