Vol. 88, No. 2, 1980

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On the existence of capillary free surfaces in the absence of gravity

Jin-Tzu Chen

Vol. 88 (1980), No. 2, 323–361

If we were to put water into a glass cylindrical container of circular cross section and transport it to outer space, the surface of the water would be uniquely determined as a lower hemisphere. Concus and Finn [1] have shown that if the circular cross section is replaced by a square section then no such surface can exist as a graph of a function. The question then arises, for what kind of cross section can we expect the existence of a surface in the form of a graph?

Mathematical Subject Classification 2000
Primary: 49F10, 49F10
Secondary: 53A10
Received: 26 September 1979
Published: 1 June 1980
Jin-Tzu Chen
Department of Mathematics
National Taiwan University