Vol. 224, No. 2, 2006

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Danzhu Shi

Abstract

A capillary surface expressible as a graph over a domain containing a protruding corner can exhibit strikingly varying behavior, with discontinuous transitions, depending on local boundary conditions. Korevaar in 1980 showed that very different kinds of behavior must be expected when the corner opening exceeds π, and later Lancaster and Siegel extended that result to indicate a remarkable range in the kinds of behavior that can occur. This work characterizes all possible modes of behavior for this case, subject to a conjecture of Concus and Finn for the protruding angle case.

Keywords

capillary surfaces, reentrant corner, corner behavior, Concus–Finn conjecture

Mathematical Subject Classification

Primary: 76B45

Secondary: 35J65, 53A10

Authors
Danzhu Shi