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Rigidity of Travelling Times for Strictly Convex Obstacles in Riemannian Manifolds
Tal Gurfinkel, Lyle Noakes, Luchezar Stoyanov
Let and be two disjoint unions of strictly convex obstacles contained within a Riemannian manifold with boundary of dimension . The sets of travelling times $\…
Uniqueness of Obstacles in Riemannian Manifolds from Travelling Times
Tal Gurfinkel, Lyle Noakes, Luchezar Stoyanov
Suppose that and are two disjoint unions of strictly convex obstacles with the same set of travelling times, contained in an -dimensional Riemannian manifold (where…
Recovering Obstacles from their Travelling Times
Tal Gurfinkel, Lyle Noakes, Luchezar Stoyanov
Noakes and Stoyanov (2021) introduced a method of recovering strictly convex planar obstacles from their set of travelling times. We provide an extension of this construction for o…
Linearisability of divergence-free fields along invariant 2-tori
David Perrella, David Pfefferlé, Luchezar Stoyanov
We find conditions under which the restriction of a divergence-free vector field to an invariant toroidal surface is linearisable. The main results are similar in conclusio…
A Stefan-Sussmann theorem for normal distributions on manifolds with boundary
David Perrella, David Pfefferlé, Luchezar Stoyanov
An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its e…
Travelling Times in Scattering by Obstacles in Curved Space
Tal Gurfinkel, Lyle Noakes, Luchezar Stoyanov
We consider travelling times of billiard trajectories in the exterior of an obstacle K on a two-dimensional Riemannian manifold M. We prove that given two obstacles with almost the…