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arXiv · 1503.02365

Asymptotics of the Weil-Petersson metric

Rafe Mazzeo·Jan Swoboda
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Abstract

We consider the Riemann moduli space $\mathcal M_{\gamma}$ of conformal structures on a compact surface of genus $\gamma>1$ together with its Weil-Petersson metric $g_{\mathrm{WP}}$. Our main result is that $g_{\mathrm{WP}}$ admits a complete polyhomogeneous expansion in powers of the lengths of the short geodesics up to the singular divisors of the Deligne-Mumford compactification of $\mathcal M_{\gamma}$.

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Rafe Mazzeo, Jan Swoboda. 2015-03-09. Asymptotics of the Weil-Petersson metric. https://arxiv.org/abs/1503.02365

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