Conformal dimension on boundary of right-angled hyperbolic buildings

TL;DR

This paper investigates the conformal dimension of the boundary of right-angled hyperbolic buildings using combinatorial modulus, establishing an optimal lower bound in the case of Fuchsian buildings.

Contribution

It introduces a method to estimate the conformal dimension of hyperbolic building boundaries using combinatorial modulus, providing an optimal bound for Fuchsian buildings.

Findings

Established an optimal lower bound for conformal dimension in Fuchsian buildings.

Connected combinatorial modulus with conformal dimension control.

Enhanced understanding of boundary geometry in hyperbolic buildings.

Abstract

In this note, we use some combinatorial modulus on the boundary of a right-angled hyperbolic building to control its conformal dimension. The lower bound obtained is optimal in the case of Fuchsian buildings.