Holomorphic motions, Assouad dimension and quasiconformal mappings
Katheryn Menssen, Malik Younsi
Abstract
We study the variation of the quasi-Assouad dimension of a set moving under a holomorphic motion. We show that the reciprocal of the quasi-Assouad dimension is inf-harmonic in the sense of Fuhrer--Ransford--Younsi. As a consequence, we obtain quasiconformal distortion bounds for quasi-Assouad dimension as well as an improved version of Smirnov's celebrated theorem on the dimension of quasicircles. Our approach is elementary in that it does not require optimal Sobolev regularity for quasiconformal mappings.
Create a lesson
Related papers
Limit theorems for Coulomb gases on a Jordan curve in an external potential
Kurt Johansson, Thomas Wolfs
On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative
Cameron MacMahon
The Reciprocal Problem on Weighted Bergman Spaces
Guangfu Cao, Li He, Shuqing Zhang
On φ-Normality of Harmonic Mappings and Their Families
Gopal Datt, Ritesh Pal
Weak Asymptotic Symmetry of Quasisymmetric Embeddings on Quasilines
Katsuhiko Matsuzaki, Fei Tao
Target Geometry in Prescribed-Value Schwarz Lemmas for Harmonic Maps
Miljan Knežević, Miodrag Mateljević