6 papers
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…
Simultaneous Optimization of Geodesics and Fréchet Means
Frederik Möbius Rygaard, Søren Hauberg, Steen Markvorsen
A central part of geometric statistics is to compute the Fréchet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian di…
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…
Score Matching Riemannian Diffusion Means
Frederik Möbius Rygaard, Steen Markvorsen, Søren Hauberg +1
Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome…