Pressure type metrics on spaces of metric graphs

Abstract

In this note, we consider two Riemannian metrics on a moduli space of metric graphs. Each of them could be thought of as an analogue of the Weil-Petersson metric on the moduli space of metric graphs. We discuss and compare geometric features of these two metrics with the "classic" Weil-Petersson metric in Teichm\"uller theory. This paper is motivated by Pollicott and Sharp's earlier work.