Renormalized volume and the volume of the convex core

Martin Bridgeman; Richard Canary

Renormalized volume and the volume of the convex core

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arxiv 1502.05018 v3 pith:YGWUIKS5 submitted 2015-02-17 math.DG math.GT

Martin Bridgeman , Richard Canary This is my paper

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keywords convexcorevolumeboundaryhyperbolicrenormalizedresultsbounds

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We obtain upper and lower bounds on the difference between the renormalized volume and the volume of the convex core of a convex cocompact hyperbolic 3-manifold which depend on the injectivity radius of the boundary of the universal cover of the convex core and the Euler characteristic of the boundary of the convex core. These results generalize results of Schlenker obtained in the setting of quasifuchsian hyperbolic 3-manifolds.

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