1997/04/30 by Francis Bonahon, Bonahon, Francis
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9704017
18 pages, 3 pictures, AmsTeX
arxiv created 1997/04/30 · openalex publication_date 1997/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 3-dimensional hyperbolic geometry, the classical Schlafli formula expresses the variation of the volume of a hyperbolic polyhedron in terms of the length of its edges and of the variation of its dihedral angles. We prove a similar formula for the variation of the volume of the convex core of a geometrically finite hyperbolic 3--manifold M, as we vary the hyperbolic metric of M. In this case, the pleating locus of the boundary of the convex core is not constant any more, but we showed in an earlier paper that the variation of the bending of the boundary of the convex core is described by a geodesic lamination with a certain transverse distribution. We prove that the variation of the volume of the convex core is then equal to 1/2 the length of this transverse distribution.