In this paper we study the Weil–Petersson geometry of , the compactified moduli space of Riemann surfaces with genus g and n marked points. The main goal of this paper is to understand the growth of the diameter of as a function of and . We show that this diameter grows as in , and is bounded above by in for some constant . We also give a lower bound on the growth in of the diameter of in terms of an auxiliary function that measures the extent to which the thick part of moduli space admits radial coordinates.
"Growth of the Weil–Petersson diameter of moduli space." Duke Math. J. 161 (1) 139 - 171, 15 January 2012. https://doi.org/10.1215/00127094-1507312