Abstract
There is an intimate connection between the problem of finding a bounded by a given non-self-intersecting curve and the problem of finding a bounded by that curve and having least possible area. The very name minimal surface arises from the fact that the differential equations of a are the Euler-Lagrange equations of the problem of least area, expressing the vanishing of the first variation of the area. Moreover, if the given curve bounds a of finite area (which is the only case for which the problem of least area has a meaning) the two problems have common solutions.1 Nevertheless, it is well known that a need not have least area for its boundary, and also that a of least area need not be minimal. The following problem therefore suggests itself: Given a S, defined by equations
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