Motivated by the large amount 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 \({\mathbb {R}}^3\) 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 one-parameter family of properly embedded annuli that are analogous to the usual minimal catenoids.

中文翻译：

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在规定的平均曲率下，将$$ {\ mathbb {R}} ^ {3} $$ R3正确浸入表面的半空间定理

出于在几个环境空间中获得最小和正恒定平均曲率曲面的大量结果的推动，本文的目的是针对\（{\ mathbb {R}} ^ 3 \ ），其平均曲率是高斯图的规定函数。为了达到这个目的，我们将研究一类正确嵌入环的一参数家族的无穷大行为，该现象类似于通常的最小链状体。