Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane

TL;DR

This paper establishes precise distortion estimates for quasiconformal mappings in the plane, focusing on their effects on Riesz capacities and Hausdorff measures, advancing understanding in geometric function theory.

Contribution

It provides the first sharp distortion bounds for quasiconformal maps concerning Riesz capacities and Hausdorff measures in the plane.

Findings

Sharp distortion estimates for Riesz capacities

Precise bounds for Hausdorff measures under quasiconformal maps

Enhanced understanding of geometric distortions in potential theory

Abstract

In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from non linear potential theory and in terms of the Hausdorff measures.