Half-space theorems for properly immersed surfaces in R3 with prescribed mean curvature

Abstract

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in R3 whose mean curvature is given as a prescribed function of its Gauss map. In order to achieve this purpose, we will study the behavior at in nity of a 1-parameter family of properly embedded annuli that are analogous to the usual minimal catenoids.