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arXiv · 2404.08942

Visual angle metric in the upper half plane

Masayo Fujimura·Oona Rainio·Matti Vuorinen
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Abstract

We prove an identity which connects the visual angle metric $v_{\mathbb{H}^2}$ and the hyperbolic metric $\rho_{\mathbb{H}^2}$ of the upper half plane $\mathbb{H}^2$. The proof is based on geometric arguments and uses computer algebra methods for formula manipulation. We also prove a sharp H\"older continuity result for quasiregular mappings with respect to the visual angle metric.

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Masayo Fujimura, Oona Rainio, Matti Vuorinen. 2024-04-13. Visual angle metric in the upper half plane. https://arxiv.org/abs/2404.08942

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