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Generalized Fermat's principle and Snell's law for cone structures and applications
Miguel Ãngel Javaloyes, Steen Markvorsen, Enrique Pendás-Recondo +1
Fermat's principle is fully generalized to the case where a smooth interface separates two cone structures -- Lorentz-Finsler lightcones -- representing wave propagation in a poten…
The convex hull of a convex space curve with four vertices
Jakob Bohr, Steen Markvorsen, Matteo Raffaelli
We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, i.e., four points of vanishing torsion, and lying on the boun…
Time-dependent Zermelo navigation with tacking
Steen Markvorsen, Enrique Pendás-Recondo, Frederik Möbius Rygaard
We address the time- and position-dependent Zermelo navigation problem within the framework of Lorentz-Finsler geometry. Since the initial work of E. Zermelo, the task is to find t…
Criteria for parabolicity and hyperbolicity of conductive Riemannian manifolds
Vicent Gimeno i Garcia, Ana Hurtado, Steen Markvorsen +1
Motivated by the physics of anisotropic conductive materials we consider a linear elliptic operator of divergence type on a Riemannian manifold . The…