Heiko von der Mosel

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We discuss the analytic properties of curves γ whose global curvature function ρG[γ ]−1 is p-integrable. It turns out that theLp-norm Up(γ ) := ‖ρG[γ ]−1‖Lp is an appropriate model for a self-avoidance energy interpolating between “soft” knot energies in form of singular repulsive potentials and “hard” self-obstacles, such as a lower bound on the global(More)
We derive the Euler-Lagrange equations for nonlinearly elastic rods with selfcontact. The excluded-volume constraint is formulated in terms of an upper bound on the global curvature of the centre line. This condition is shown to guarantee the global injectivity of the deformation of the elastic rod. Topological constraints such as a prescribed knot and link(More)
Hypersurfaces of prescribed weighted mean curvature, or F -mean curvature, are introduced as critical immersions of anisotropic surface energies, thus generalizing minimal surfaces and surfaces of prescribed mean curvature. We first prove enclosure theorems in R for such surfaces in cylindrical boundary configurations. Then we derive a general second(More)
We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of closed curves in IR3 to model the elastic behaviour of knotted loops of springy wire. A potential of Coulomb type with a small factor as a measure for the thickness of the wire is added to the elastic energy in order to preserve the isotopy class. With a direct method(More)
What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope’s thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing(More)
We prove the existence of conformally parametrized minimizers for parametric two-dimensional variational problems subject to partially free boundary conditions. We establish regularity of class H loc ∩C1,α, 0 < α < 1, up to the free boundary under the assumption that there exists a perfect dominance function in the sense of C.B. Morrey. Mathematics Subject(More)
Quantitative data of hydroxycinnamic acids, hydroxybenzoic acids and hydroxycoumarins (after hydrolysis of derivatives) and of catechins are given. -Large quantities of catechins and hydroxycinnamic acid derivatives are found in the young fruit. Related to mg per kg fresh weight these concentrations soon decline sharply, especially during the progressive(More)