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Visual angle metric in the upper half plane (2404.08942v2)
Published 13 Apr 2024 in math.MG
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.