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math.DS2025
Interacting Geodesics on Discrete Manifolds
Oliver Knill
We define an evolution of multiple particles on a discrete manifold . Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move…
math.CO2025
Geodesics for Discrete manifolds
Oliver Knill
The geodesic flow on a finite discrete q-manifold with or without boundary is defined as as a permutation of its ordered q-simplices. This allows to define geodesic sheets and a no…
math.DG2025
Density of wave fronts
Emily Kang, Oliver Knill
We prove that wave fronts on a flat torus become dense. As a corollary, wave fronts become dense for a square billiard or for the geodesic flow on the flat Klein bottle or the cube…