On volumes of quaternionic hyperbolic n-orbifolds

TL;DR

This paper derives an explicit lower volume bound for quaternionic hyperbolic orbifolds based on dimension, utilizing Wang's bound on embedded ball radii in fundamental domains.

Contribution

It provides a new, explicit lower volume bound for quaternionic hyperbolic orbifolds depending solely on their dimension.

Findings

Established a dimension-dependent lower volume bound.

Utilized Wang's bound to relate geometric properties to volume.

Contributed to the understanding of orbifold volume constraints.

Abstract

By use of H. C. Wang's bound on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group, we construct an explicit lower bound for the volume of a quaternionic hyperbolic orbifold that depends only on dimension.