On distortion of quasiregular mappings of the upper half plane
Masayo Fujimura, Matti Vuorinen
TL;DR
This paper establishes a precise distortion estimate for hyperbolic metrics under K-quasiregular mappings of the upper half plane, utilizing novel inequalities and a Schwarz lemma adapted for quasiregular functions.
Contribution
It introduces a new Bernoulli inequality and applies a Schwarz lemma to derive sharp distortion bounds for quasiregular mappings.
Findings
Proved a sharp distortion inequality for hyperbolic metrics
Developed a new Bernoulli inequality for quasiregular mappings
Extended Schwarz lemma techniques to quasiregular context
Abstract
We prove a sharp result for the distortion of a hyperbolic type metric under -quasiregular mappings of the upper half plane. The proof makes use of a new kind of Bernoulli inequality and the Schwarz lemma for quasiregular mappings.
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Taxonomy
TopicsAnalytic and geometric function theory · Differential Equations and Boundary Problems · Algebraic and Geometric Analysis