  By using Stationary-to-Randers correspondence (SRC), a characterization of
light and time-convexity of the boundary of a region of a standard stationary
(n+1)-spacetime is obtained, in terms of the convexity of the boundary of a
domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is
analyzed in depth and, as a consequence, the causal simplicity and the
existence of causal geodesics confined in the region and connecting a point to
a stationary line are characterized. Applications to asymptotically flat
spacetimes include the light-convexity of stationary hypersurfaces which
project in a spacelike section of an end onto a sphere of large radius, as well
as the characterization of their time-convexity with natural physical
interpretations. The lens effect of both light rays and freely falling massive
particles with a finite lifetime, (i.e. the multiplicity of such connecting
curves) is characterized in terms of the focalization of the geodesics in the
underlying Randers manifolds.
