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Non-continuous
dependence of surfaces of least area on the boundary
curve
Michael James Beeson |
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Vol. 70 (1977), No. 1, 11–17
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Abstract |
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In this paper, we consider the question of continuous dependence associated with the following version of Plateau’s problem: Given a (sufficiently smooth) Jordan curve Γ, find a surface of least area bounded by Γ. In other words, we ask whether a surface SΓ of least area among surfaces bounded by Γ can be found, continuously in Γ. The answer is no; in fact, sometimes one does not even have local continuous dependence. That is, for certain curves Γ0, one cannot find SΓ continuously in Γ, even on any neighborhood of Γ0. |
Mathematical Subject Classification 2000
Primary: 53A10
Secondary: 58E15, 49F10
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Milestones
Received: 4 November 1975
Published: 1 May 1977
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Authors |
| Michael James Beeson | |
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