Non existence and existence of capillary surfaces
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It is shown that a curvature condition on the boundary of a convex domain ω, shown in  to suffice for existence of a solution of the capillary equation in ω, does not suffice without the convexity condition; this is so even in cases for which the negative curvatures that appear may be arbitrarily small in magnitude.
The “trapezoid” example of the preceding note is also considered, and a sense is indicated in which the local criterion of  is sufficient for existence of a solution.
KeywordsNumber Theory Algebraic Geometry Topological Group Convex Domain Negative Curvature
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