  For a Riemannian manifold $(M,g)$ with strictly convex boundary $\partial M$,
the lens data consists in the set of lengths of geodesics $\gamma$ with
endpoints on $\partial M$, together with their endpoints $(x_-,x_+)\in \partial
M\times \partial M$ and tangent exit vectors $(v_-,v_+)\in T_{x_-} M\times
T_{x_+} M$. We show deformation lens rigidity for a large class of manifolds
which includes all manifolds with negative curvature and strictly convex
boundary, possibly with non-trivial topology and trapped geodesics. For the
same class of manifolds in dimension $2$, we prove that the set of endpoints
and exit vectors of geodesics (ie. the scattering data) determines the topology
and the conformal class of the surface.
