Minimal entropy for uniform lattices in product of hyperbolic planes

Abstract

Let $M$ be a quotient of ${\mathbb{H}}^2\times \cdots \times {\mathbb{H}}^2$ (product of hyperbolic planes) by a uniform lattice of $({\mathrm{PSL}}_2(\mathbb{R}){)}^n$. We prove that, among metrics of $M$ of prescribed volume, the sum of hyperbolic metrics has minimal volume entropy.