# 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}
}
• Antonio Bueno
• Published 6 October 2020
• Mathematics
• Annals of Global Analysis and Geometry
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
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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
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