Uniqueness of Obstacles in Riemannian Manifolds from Travelling Times
arXiv (Cornell University)(2023)
Abstract
Suppose that $K$ and $L$ are two disjoint unions of strictly convex obstacles with the same set of travelling times, contained in an $n$-dimensional Riemannian manifold $M$ (where $n\geq2$). Under some natural curvature conditions on $M$, and provided that no geodesic intersects more than two components in $K$ or $L$, we show that $K = L$.
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Key words
riemannian manifolds,obstacles,travelling times,uniqueness
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