Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
نویسندگان
چکیده
منابع مشابه
The asymptotic shape of a boundary layer of symmetric Willmore surfaces of revolution*
We consider the Willmore boundary value problem for surfaces of revolution over the interval [−1, 1] where, as Dirichlet boundary conditions, any symmetric set of position α and angle tanβ may be prescribed. Energy minimising solutions uα,β have been previously constructed and for fixed β ∈ R, the limit limαց0 uα,β(x) = √ 1 − x has been proved locally uniformly in (−1, 1), irrespective of the b...
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We study a boundary value problem for Willmore surfaces of revolution, where the position and the mean curvature H = 0 are prescribed as boundary data. The latter is a natural datum when considering critical points of the Willmore functional in classes of functions where only the position at the boundary is fixed. For specific boundary positions, catenoids and a suitable part of the Clifford to...
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where H is the mean curvature of the immersion and K its Gauss curvature. This functional models the elastic energy of thin shells. Willmore studied in [7] the functional W0, by now called Willmore functional. First we note that Wγ(Γ) ≥ 0 holds for every γ ∈ [0, 1]. Let κ1, κ2 ∈ R denote the principal curvatures of the surface. Then H − γK = 1 4 (κ1 + κ2) 2 − γκ1 · κ2 = 1−γ 4 (κ1 + κ2) 2 + γ 4 ...
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The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surf...
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Abstract : We found a new formulation to the Euler-Lagrange equation of the Willmore functional for immersed surfaces in R. This new formulation of Willmore equation appears to be of divergence form, moreover, the nonlinearities are made of jacobians. Additionally to that, if ~ H denotes the mean curvature vector of the surface, this new form writes L ~ H = 0 where L is a well defined locally i...
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ژورنال
عنوان ژورنال: Advances in Calculus of Variations
سال: 2011
ISSN: 1864-8258,1864-8266
DOI: 10.1515/acv.2010.022