Hyperbolic volume of n-manifolds with geodesic boundary and orthospectra

In this paper we describe a function $F_n:{\mathbf{R}}_{+}\to {\mathbf{R}}_{+}$ such that for any hyperbolic n-manifold $M$ with totally geodesic boundary $\partial M \neq \emptyset$,thevolumeof$M$isequaltothesumofthevaluesof$F_n$onthe\text{em}orthospectrumof$M$\mathrm{.}Wederiveanintegralformulafor$F_n$ in terms of elementary functions. We use this to give a lower bound for the volume of a hyperbolic n-manifold with totally geodesic boundary in terms of the area of the boundary.