40 citations · 107 across the 10 of their papers we have counts for
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On some knot energies involving Menger curvature
Paweł Strzelecki, Marta Szumańska, Heiko von der Mosel
We investigate knot-theoretic properties of geometrically defined curvature energies such as integral Menger curvature. Elementary radii-functions, such as the circumradius of thre…
Characterizing ~submanifolds by -integrability of global curvatures
Sławomir Kolasiński, Paweł Strzelecki, Heiko von der Mosel
We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold of class and of arbitrary dimension and codimen…
Tangent-point repulsive potentials for a class of non-smooth -dimensional sets in . Part I: Smoothing and self-avoidance effects
Pawel Strzelecki, Heiko von der Mosel
We consider repulsive potential energies $\E_q(Σ)$, whose integrand measures tangent-point interactions, on a large class of non-smooth -dimensional sets in Finitene…
Tangent-point self-avoidance energies for curves
Pawel Strzelecki, Heiko von der Mosel
We study a two-point self-avoidance energy which is defined for all rectifiable curves in as the double integral along the curve of . Here stands for the rad…
Integral Menger curvature for surfaces
Pawel Strzelecki, Heiko von der Mosel
We develop the concept of integral Menger curvature for a large class of nonsmooth surfaces. We prove uniform Ahlfors regularity and a -a-priori bound for surfaces for whi…