Quasiconformal distortion of the lower dimension and applications
Efstathios Konstantinos Chrontsios Garitsis Jeremy T. Tyson
作者信息
Abstract
We study the distortion of the lower dimension and lower spectrum of sets under quasiconformal mappings. As an application, we verify weighted Hardy--Sobolev inequalities in Euclidean domains arising as quasiconformal images of domains with sufficiently regular boundaries. The regularity in question is phrased in terms of estimates for either the Assouad or the lower dimension of the complement. We also provide dilatation-dependent classification results for certain planar open sets.引用本文复制引用
Efstathios Konstantinos Chrontsios Garitsis,Jeremy T. Tyson.Quasiconformal distortion of the lower dimension and applications[EB/OL].(2026-11-03)[2026-11-05].https://arxiv.org/abs/2611.05118.学科分类
数学
|国家预印本平台