Explicit upper bound for the Weil-Petersson volumes
Abstract
An explicit upper bound for the Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces is obtained, using Penner's combinatorial integration scheme with embedded trivalent graphs. It is shown that for a fixed number of punctures n and for genus g going to infinity, the Weil-Petersson volume of Mg,n has an upper bound cg g2g. Here c is an independent of n constant, which is given explicitly.
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