Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces
Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces
The Weil-Petersson and Takhtajan-Zograf metrics on the Riemann moduli spaces of complex structures for an $n$-fold punctured oriented surface of genus $g,$ in the stable range $g+2n>2,$ are shown here to have complete asymptotic expansions in terms of Fenchel-Nielsen coordinates at the exceptional divisors of the Knudsen-Deligne-Mumford compactification. This is …