Universal locally univalent functions and universal conformal metrics with constant curvature

Daniel Pohl; Oliver Roth

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arXiv · 1709.10454

Universal locally univalent functions and universal conformal metrics with constant curvature

Daniel Pohl·Oliver Roth

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Abstract

We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk. These results are used to prove that on any hyperbolic simply connected plane domain there exist universal conformal metrics with prescribed constant curvature.

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Daniel Pohl, Oliver Roth. 2018-04-03. Universal locally univalent functions and universal conformal metrics with constant curvature. https://arxiv.org/abs/1709.10454

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