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

  title={Properly embedded surfaces with prescribed mean curvature in 
              \$\$\{\mathbb \{H\}\}^2\times \{\mathbb \{R\}\}\$\$
  author={Antonio Bueno},
  journal={Annals of Global Analysis and Geometry},
  • 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… 
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