Addendum to: On Volumes of Arithmetic Quotients of SO(1,n)

TL;DR

This paper corrects previous errors in the proof regarding the uniqueness of minimal covolume arithmetic subgroups of SO(1,n), confirms some conjectured results, and discusses potential future research directions.

Contribution

It provides a corrected proof of the uniqueness of minimal covolume arithmetic subgroups and establishes some conjectured results in the field.

Findings

Corrected proof of subgroup uniqueness

Confirmation of conjectured results

Remarks on future research directions

Abstract

There are errors in the proof of the uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.