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math.MG2025
Visual angle metric in the upper half plane
Masayo Fujimura, Oona Rainio, Matti Vuorinen
We prove an identity which connects the visual angle metric and the hyperbolic metric of the upper half plane . The proof is ba…
math.MG2024
Collinearity of points on Poincaré unit disk and Riemann sphere
Masayo Fujimura, Oona Rainio, Matti Vuorinen
We study certain points significant for the hyperbolic geometry of the unit disk. We give explicit formulas for the intersection points of the Euclidean lines and the stereographic…
math.MG2024
Inequalities for a new hyperbolic type metric
Oona Rainio
We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequali…