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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the area of harmonic surfaces

Author: Michael Beeson
Journal: Proc. Amer. Math. Soc. 69 (1978), 143-147
MSC: Primary 58E15; Secondary 49F25, 53A10
MathSciNet review: 0482818
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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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Article copyright: © Copyright 1978 American Mathematical Society