Asymptotic dilation of regular homeomorphisms

TL;DR

This paper investigates the asymptotic behavior of regular homeomorphisms near zero, using length-area functionals and angular dilatations, with applications to solutions of nonlinear Beltrami equations.

Contribution

It introduces new asymptotic estimates for regular homeomorphisms and applies these to nonlinear Beltrami equations, expanding understanding of their boundary behavior.

Findings

Asymptotic ratio |f(z)|/|z| analyzed as z→0

Use of length-area functionals and angular dilatations

Applications to nonlinear Beltrami equations

Abstract

We study the asymptotic behavior of the ratio $|f(z)|/|z|$ as $z\to 0$ for mappings differentiable a.e. in the unit disc with non-degenerated Jacobian. The main tools involve the length-area functionals and angular dilatations depending on some real number $p.$ The results are applied to homeomorphic solutions of a nonlinear Beltrami equation. The estimates are illustrated by examples.