Abstract
The aim of this paper is to extend classic results of the theory of constant mean curvature surfaces in the product space \({\mathbb {H}}^2\times {\mathbb {R}}\) to the class of immersed surfaces whose mean curvature is given as a \(C^1\) 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.
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Notes
In [9] z stands for a complex parameter for the first fundamental form.
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The author was partially supported by MICINN-FEDER Grant No. MTM2016-80313-P and Junta de Andalucía Grant No. FQM325.
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Bueno, A. Properly embedded surfaces with prescribed mean curvature in \({\mathbb {H}}^2\times {\mathbb {R}}\). Ann Glob Anal Geom 59, 69–80 (2021). https://doi.org/10.1007/s10455-020-09741-6
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DOI: https://doi.org/10.1007/s10455-020-09741-6