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We prove that if two non-trapping obstacles in $mathbb{R}^n$ satisfy some rather weak non-degeneracy conditions and the scattering rays in their exteriors have (almost) the same travelling times or (almost) the same scattering length spectrum, then they coincide.
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two obstacles satis
It was proved in cite{NS1} that obstacles $K$ in $R^d$ that are finite disjoint unions of strictly convex domains with $C^3$ boundaries are uniquely determined by the travelling times of billiard trajectories in their exteriors and also by their so c
The quantum scattering by smooth bodies is considered for small and large values of $kd$, with $k$ the wavenumber and $d$ the scale of the body. In both regimes, we prove that the forward scattering exceeds the backscattering. For high $k$, we need to assume that the body is strictly convex.
In light of the Suita conjecture, we explore various rigidity phenomena concerning the Bergman kernel, logarithmic capacity, Greens function, and Euclidean distance and volume.
We prove resolvent estimates for semiclassical operators such as $-h^2 Delta+V(x)$ in scattering situations. Provided the set of trapped classical trajectories supports a chaotic flow and is sufficiently filamentary, the analytic continuation of the