On nonnegatively curved hypersurfaces in hyperbolic space
  In this paper we prove the conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily properly embedded. 
Vincent Bonini, Shiguang Ma, and Jie Qing
math.DG