On the area of harmonic surfaces

Beeson, Michael

doi:10.1090/S0002-9939-1978-0482818-0

On the area of harmonic surfaces
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Proc. Amer. Math. Soc. 69 (1978), 143-147 Request permission

Abstract:

We prove that if the sequence ${S_n}$ of harmonic surfaces converges to the harmonic surface S, and if the boundary of ${S_n}$ is a rectifiable Jordan curve ${C_n}$, whose length is uniformly bounded by L, then the area $A({S_n})$ converges to $A(S)$. This solves an old problem, several special cases of which have been solved in the literature.

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Plateau’s problem and constructive mathematics

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