Around the Combinatorial Unit Ball of Measured Foliations on Bordered Surfaces

Abstract

The volume of the unit ball - with respect to the combinatorial length function - of the space of measured foliations on a stable bordered surface appears as the prefactor of the polynomial growth of the number of multicurves on. We find the range of for which, as a function over the combinatorial moduli spaces, is integrable with respect to the Kontsevich measure. The results depend on the topology of, in contrast with the situation for hyperbolic surfaces where [6] recently proved an optimal square integrability.