An explicit upper bound for Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces

An explicit upper bound for the Weil-Petersson volumes of punctured Riemann surfaces is obtained using Penner's combinatorial integration scheme from [4]. It is shown that for a fixed number of punctures n and for genus g increasing, lim(g --> infinity, n fixed) ln vol(W P) (M-g,(n))/g ln g less than or equal to 2, while this limit is exactly equal to two for n = 1.