The Asymptotic Behavior of Embedded Minimal Surfaces of Finite Total Curvature

We prove that the catenoid-type ends of the CostaHoffman-Meeks minimal surfaces are asymptotic to ends of two catenoids that differ by a nontrivial vertical translation. Thus the "desingularization" of the union of the catenoid and the plane induces a vertical separation of the ends of the catenoid.