Approximate Formulae for Willmore Surfaces via Support Functions and Matlab
نویسندگان
چکیده
منابع مشابه
Generalized Weierstrass Formulae, Soliton Equations and Willmore Surfaces I. Tori of Revolution and the Mkdv Equation
A new approach is proposed for study structure and properties of the total squared mean curvature W of surfaces in R 3. It is based on the generalized Weierstrass formulae for inducing surfaces. The quantity W (Will-more functional or extrinsic Polyakov action) is shown to be invariant under the modified Novikov–Veselov hierarchy of integrable flows. It is shown that extremals of W (Willmore su...
متن کاملConstrained Willmore Surfaces
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...
متن کامل5 Constrained Willmore Surfaces
We develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ HdA 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 surfaces in space forms.
متن کاملAnalysis Aspects of Willmore Surfaces
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...
متن کامل2 00 8 Constrained Willmore Surfaces
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W = R H 2 under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of immersions under ...
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ژورنال
عنوان ژورنال: American Journal of Undergraduate Research
سال: 2016
ISSN: 1536-4585,2375-8732
DOI: 10.33697/ajur.2016.006