Corpus ID: 218502279

# Proper superminimal surfaces of given conformal types in the hyperbolic four-space

@article{Forstneri2020ProperSS,
title={Proper superminimal surfaces of given conformal types in the hyperbolic four-space},
author={F. Forstneri{\vc}},
journal={arXiv: Differential Geometry},
year={2020}
}
Let $H^4$ denote the hyperbolic four-space. Given a bordered Riemann surface, $M$, we prove that every smooth conformal superminimal immersion $\overline M\to H^4$ can be approximated uniformly on compacts in $M$ by proper conformal superminimal immersions $M\to H^4$. In particular, $H^4$ contains properly immersed conformal superminimal surfaces normalised by any given open Riemann surface of finite topological type without punctures. The proof uses the analysis of holomorphic Legendrian… Expand
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