The Bridgeman–Kahn identity for hyperbolic manifolds with cusped boundary

Original Paper


In this note, we extend the Bridgeman–Kahn identity to all finite-volume orientable hyperbolic n-manifolds with totally geodesic boundary. In the compact case, Bridgeman and Kahn are able to express the manifold’s volume as the sum of a function over only the orthospectrum. For manifolds with non-compact boundary, our extension adds terms corresponding to intrinsic invariants of boundary cusps.


Hyperbolic manifold Geodesic boundary Orthospectrum Geometric identities 

Mathematics Subject Classification

57M50 30F40 32Q45 


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Mathematics Research UnitMaison du NombreEsch-sur-AlzetteLuxembourg

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