Holomorphic motions, dimension, area and quasiconformal mappings

2023/02/15 by Aidan Fuhrer, Thomas Ransford, Fuhrer, Aidan +3 · 1 citation
Mathematics · #28A78 (Secondary) #30C62 #31A05 #37F44 (Primary) #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2302.07743

openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a new, unified approach to various celebrated theorems about quasiconformal mappings, including the work of Astala on the distortion of area and dimension under quasiconformal mappings and the work of Smirnov on the dimension of quasicircles.

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• Sobolev and quasiconformal distortion of intermediate dimension with applications to conformal dimension

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