3 papers
math.DG2026
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…
gr-qc2026
On the formulations of the Fermat principle in general relativity and beyond
Erasmo Caponio, Miguel Angel Javaloyes
This paper presents a survey of the Fermat principle within the framework of general relativity, tracing its evolution from classical optics to its modern variational formulation i…
math.DG2024
Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system
Erasmo Caponio, Miguel Angel Javaloyes, Antonio Masiello
We consider a geodesic problem in a manifold endowed with a Randers-Kropina metric. This is a type of singular Finsler metric arising both in the description of the lightlike vecto…