On the area of harmonic surfaces
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- by Michael Beeson
- Proc. Amer. Math. Soc. 69 (1978), 143-147
- DOI: https://doi.org/10.1090/S0002-9939-1978-0482818-0
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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.References
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Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 143-147
- MSC: Primary 58E15; Secondary 49F25, 53A10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0482818-0
- MathSciNet review: 0482818