Analytic mappings of the unit disk which almost preserve hyperbolic area

2024/03/05 by Ivrii, Oleg, Nicolau, Artur · 3 citations
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.02798

Abstract

In this paper, we study analytic self-maps of the unit disk which distort hyperbolic area of large hyperbolic disks by a bounded amount. We give a number of characterizations involving angular derivatives, Lipschitz extensions, Möbius distortion, the distribution of critical points and Aleksandrov-Clark measures. We also study Lyapunov exponents of their Aleksandrov-Clark measures.

Cited by

• Carleson Measures, Vanishing Mean Oscillation and Critical Points
• Analytic mappings of the unit disk with bounded compression
• A Burns-Krantz type theorem for Blaschke products

Related

• Analytic mappings of the unit disk with bounded compression
• Level sets of the Hyperbolic Derivative for analytic self-maps of the unit disk
• Boundary distortion estimates for holomorphic maps
• Rigidity of Analytic Functions at the Boundary
• Hyperbolic distortion and conformality at the boundary