The aim of this paper is to extend classic results of the theory of constant mean curvature surfaces in the product space $${\mathbb {H}}^2\times {\mathbb {R}}$$ H 2 × R to the class of immersed surfaces whose mean curvature is given as a $$C^1$$ C 1 function depending on their angle function. We cover topics such as the existence of a priori curvature and height estimates for graphs and a structure-type result, which classifies properly embedded surfaces with finite topology and at most one end.

中文翻译：

---

在 $${\mathbb {H}}^2\times {\mathbb {R}}$$ 中正确嵌入具有规定平均曲率的曲面

本文的目的是将乘积空间 $${\mathbb {H}}^2\times {\mathbb {R}}$$ H 2 × R 中常平均曲率曲面理论的经典结果推广到一类浸没表面，其平均曲率由 $$C^1$$ C 1 函数给出，具体取决于它们的角度函数。我们涵盖了诸如图的先验曲率和高度估计的存在以及结构类型结果等主题，该结果对具有有限拓扑和至多一端的适当嵌入表面进行分类。