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.The author was partially supported by MICINN-FEDER Grant No. MTM2016-80313-P, Junta de
Andalucía Grant No. FQM325 and FPI-MINECO Grant No. BES-2014-067663
