Scalar curvature and volume entropy of hyperbolic 3-manifolds

Abstract

We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this construction gives counterexamples to a conjecture of I. Agol, P. Storm and W. Thurston.

v3 update: some details are added. 15 pages, 2 figures. Final version, accepted by JEMS