Moments of a length function on the boundary of a hyperbolic manifold (Q498725)

Let \(M\) be an \(n\)-dimensional compact hyperbolic manifold with nonempty totally geodesic boundary. Then one can define a measurable function \(L:\partial M \rightarrow \mathbb{R}\) by \(L(x)=\mathrm{length}(\alpha_x)\) for \(x \in \partial M\) and \(\alpha_x\) is the geodesic emanating from \(x\) normal to \(\partial M\). In the paper under review, the author shows that \(A_k(M)\) is finite for all nonnegative integers \(k\), where \(A_k(M)\) is the \(k^{\mathrm{th}}\) moment of \(L\). In addition, the author finds a formula of \(A_k(M)\) in terms of the orthospectrum and clarifies a relation between this formula and Bridgeman's identity and Basmajian's identity.