Minimal surfaces in finite volume non compact hyperbolic $3$-manifolds
  We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic $3$-manifold $\mathcal{N}$. We also obtain a least area, incompressible, properly embedded, finite topology, $2$-sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This determines its asymptotic behavior. Some rigidity theorems are obtained. 
Pascal Collin, Laurent Hauswirth, Laurent Mazet, Harold Rosenberg
math.DG