Hilbert metric and Hölder continuity

2025/11/27 by Altınkaya, Şahsene, Fujimura, Masayo, Mocanu, Marcelina +1
#30C62 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.22591

Abstract

We prove several formulas for the Hilbert metric in the unit disk and apply these results to study quasiregular mappings of the unit disk \mathbbB² onto a bounded convex domain D. The main result deals with the Hölder continuity of these mappings with respect to Hilbert metrics of \mathbbB² and D. Also several open problems are formulated.

Citations

• On families of Finsler metrics
• Hilbert metric and quasiconformal mappings
• Formulas for the visual angle metric
• On cyclic quadrilaterals in euclidean and hyperbolic geometries

Related

• Hilbert metric and quasiconformal mappings
• Hilbert metrics and Minkowski norms
• Isometries of the Hilbert Metric
• A specific model of Hilbert geometry on the unit disc
• Quasiconformal mappings and Hölder continuity