For every n≥3 there are infinitely many pairwise incommensurable finite-volume hyperbolic n-manifolds with totally geodesic boundary sharing one fixed perimeter-to-volume ratio.
Non-linear residually finite groups
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Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio
For every n≥3 there are infinitely many pairwise incommensurable finite-volume hyperbolic n-manifolds with totally geodesic boundary sharing one fixed perimeter-to-volume ratio.