  We prove global Strichartz estimates without loss outside two strictly convex
obstacles, combining arguments from M.Ikawa (1982,1988) with more recent ones
inspired by N.Burq, C.Guillarmou, and A. Hassell (2010) and O. Ivanovici
(2010). This is to be contrasted with the loss in the smoothing estimate for
the Schr\"odinger equation with Dirichlet boundary conditions in the presence
of a trapped geodesic.
