Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio

Abstract

We exhibit, for any $n\ge 3$, infinitely many pairwise incommensurable complete finite-volume hyperbolic $n$-manifolds, both compact and noncompact, each with nonempty totally geodesic boundary and all sharing the same perimeter-to-volume ratio.

6 pages, 1 figure. Comments welcome