ATTACHING HANDLES TO CONSTANT-MEAN-CURVATURE-1 SURFACES IN HYPERBOLIC 3-SPACE

Abstract

Complete minimal surfaces and constant mean curvature surfaces in Euclidean or hyperbolic space have been the object of much attention in recent years and particular efforts have been devoted in understanding the moduli space of these objects. More precisely, the surfaces we are interested in are complete, noncompact surfaces which may or may not be embedded but enjoy the somehow weaker (and slightly different) property to be Alexandrov embedded. Since we do not need this notion later on in the paper, we simply refer to [6] or [12] for a precise definition of Alexandrov embeddedness.