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Projectability and
uniqueness of F-stable
immersions with partially free boundaries
Frank Müller and Sven Winklmann |
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Vol. 230 (2007), No. 2, 409–426
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Abstract |
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We study immersed critical points X of an elliptic parametric functional ℱ(X) = ∫ BF(Xu ∧Xv)dudv that are spanned into a partially free boundary configuration {Γ,𝒮} in ℝ3. We suppose that 𝒮 is a cylindrical support surface and that Γ is a closed Jordan arc with a simple convex projection. Under geometrically reasonable assumptions on {Γ,𝒮}, F, and X we prove the projectability and uniqueness of stable immersions. This generalizes a result for minimal surfaces obtained by Hildebrandt and Sauvigny. |
Keywords
F-minimal immersions, partially free boundaries,
uniqueness, projectability, Wulff shape
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Mathematical Subject Classification 2000
Primary: 53C42, 35J65, 49Q10
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Milestones
Received: 25 August 2005
Accepted: 15 May 2006
Published: 1 April 2007
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Authors |
| Frank Müller | |
| Brandenburgische Technische
Universität Cottbus Institut für Mathematik Konrad-Zuse-Straße 1 03044 Cottbus Germany |
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| Sven Winklmann | |
| Universität Duisburg-Essen Campus Duisburg Fachbereich Mathematik 47048 Duisburg Germany |
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| http://www.uni-duisburg.de/FB11/DGL/Winklmann/wink | |
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