# Properly embedded surfaces with prescribed mean curvature in $${\mathbb {H}}^2\times {\mathbb {R}}$$ H

@article{Bueno2020ProperlyES, title={Properly embedded surfaces with prescribed mean curvature in \$\$\{\mathbb \{H\}\}^2\times \{\mathbb \{R\}\}\$\$ H }, author={Antonio Bueno}, journal={Annals of Global Analysis and Geometry}, year={2020}, volume={59}, pages={69-80} }

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…

## 2 Citations

### Rotational surfaces with prescribed mean curvature in $$\mathbb {H}^2\times \mathbb {R}$$

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2021

In this paper we study rotational surfaces in the space $\mathbb{H}^2\times\mathbb{R}$ whose mean curvature is given as a prescribed function of their angle function. These surfaces generalize, among…

### Delaunay Surfaces of Prescribed Mean Curvature in $$\mathrm {Nil}_3$$ and $$\widetilde{SL_2}(\mathbb {R})$$

- MathematicsThe Journal of Geometric Analysis
- 2022

We obtain a classification result for rotational surfaces in the Heisenberg space and the universal cover of the special linear group, whose mean curvature is given as a prescribed C function…

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