Balls in quaternionic hyperbolic manifolds

Abstract

By use of the Zassenhaus neighborhood of Sp(n,1), we obtain an explicit lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifold $\mathcal{M}$ = H_Hⁿ/Γ. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds.