Spectral gap for obstacle scattering in dimension 2

We study the problem of scattering by several strictly convex obstacles, with smooth boundary and satisfying a noneclipse condition.We show, in dimension 2 only, the existence of a spectral gap for the meromorphic continuation of the Laplace operator outside the obstacles.The proof of this result relies on a reduction to an open hyperbolic quantum map, achieved by Nonnenmacher et al. (Ann. of Math.(2) 179:1 (2014), 179-251).In fact, we obtain a spectral gap for this type of object, which also has applications in potential scattering.The second main ingredient of this article is a fractal uncertainty principle.We adapt the techniques of Dyatlov et al. (J.Amer.Math.Soc.35:2 (