English

Half-space theorems for properly immersed surfaces in $\mathbb{R}^3$ with prescribed mean curvature

Differential Geometry 2019-01-15 v1

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\mathbb{R}^3 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 infinity of a 1-parameter family of properly embedded annuli that are analogous to the usual minimal catenoids.

Keywords

Cite

@article{arxiv.1901.04343,
  title  = {Half-space theorems for properly immersed surfaces in $\mathbb{R}^3$ with prescribed mean curvature},
  author = {Antonio Bueno},
  journal= {arXiv preprint arXiv:1901.04343},
  year   = {2019}
}