Ahlfors-David regularity of intrinsically quasi-symmetric sections in metric spaces

TL;DR

This paper introduces a new class of intrinsically quasi-symmetric sections in metric spaces and proves their Ahlfors-David regularity, generalizing previous concepts of intrinsically Lipschitz graphs.

Contribution

It defines intrinsically quasi-symmetric sections and establishes their Ahlfors-David regularity, extending prior work on intrinsically Lipschitz graphs in metric spaces.

Findings

Proves Ahlfors-David regularity for the new class of sections.

Generalizes the notion of intrinsically Lipschitz graphs.

Focuses on the graph property rather than the map property.

Abstract

We introduce a definition of intrinsically quasi-symmetric sections in metric spaces and we prove the Ahlfors-David regularity for this class of sections. We follow a recent result by Le Donne and the author where we generalize the notion of intrinsically Lipschitz graphs in the sense of Franchi, Serapioni and Serra Cassano. We do this by focusing our attention on the graph property instead of the map one.