منابع مشابه
Isothermic Surfaces and Hopf Cylinders
Based on the work of Pinkall, characterizations of spherical curves are given whose corresponding Hopf cylinders are isothermic surfaces in the threedimensional sphere. Comparing these characterizations with results of Langer and Singer about elastic spherical curves we determine all isothermic Willmore Hopf tori.
متن کاملExistence of Biharmonic Curves and Symmetric Biharmonic Maps
where n is the exterior normal direction of ∂Ω. In other words, we look for a “best” way to extend the boundary value φ with the prescribed normal derivative ψ. Typical examples of Ω and N are the unit ball and the unit sphere, respectively. In this case, ψ : ∂Ω → TφN means φ (x) · ψ (x) = 0 for all |x| = 1. With the given Dirichlet data φ, the most natural extension is perhaps the harmonic map...
متن کاملBiharmonic Coordinates
Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data from the boundary of a planar domain to its interior. Many different recipes for barycentric coordinates exist, some offering the convenience of a closedform expression, some providing other desirable properties at the expen...
متن کاملOn Conformal Biharmonic Immersions
This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a 2-parameter family of non-minimal conformal biharmonic immersions of cylinder into R and ...
متن کاملBiharmonic pattern selection.
A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements u. The model is based on the biharmonic equation ∇u = 0 in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson grow...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1998
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181071748