Minimal entropy for uniform lattices in PSL${}_2(\mathbb{R}{)}^n$

Abstract

We prove that, among metrics on a compact quotient of ${\left({\mathbb{H}}^2\right)}^n$ (product of hyperbolic planes) of prescribed total volume, the product of hyperbolic metrics has minimal volume entropy.

22 pages. The case with more factors ${\mathbb{H}}^2$ is now investigated