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Proceedings of the American Mathematical Society

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

 

 

The least area bounded by multiples of a curve


Author: Brian White
Journal: Proc. Amer. Math. Soc. 90 (1984), 230-232
MSC: Primary 49F20
DOI: https://doi.org/10.1090/S0002-9939-1984-0727239-0
MathSciNet review: 727239
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Abstract: For each positive integer $ n$, we construct a smooth curve $ \Gamma $ in $ {{\mathbf{R}}^4}$ such that the least area of a surface (integral current) with boundary $ n\Gamma $ is less than $ n/k$ of the least area of a surface with boundary $ k\Gamma \left( {1 \leqslant k < n} \right)$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0727239-0
Article copyright: © Copyright 1984 American Mathematical Society