Ford fundamental domains in symmetric spaces of rank one

TL;DR

This paper proves the existence of Ford fundamental domains for broad classes of subgroups in rank one symmetric spaces, extending previous results without relying on space classification.

Contribution

It establishes the existence of isometric fundamental regions in rank one symmetric spaces for many subgroups, generalizing prior specific cases without using space classification.

Findings

Existence of Ford fundamental domains for large classes of subgroups.

The proof does not depend on the classification of symmetric spaces.

Unifies and extends previous known results.

Abstract

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and domains are essentially subsumed by our work.