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Mazzeo, Rafe; Swoboda, Jan (2017): Asymptotics of the Weil-Petersson Metric. In: International Mathematics Research Notices, No. 6: pp. 1749-1786
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Weconsider the Riemann moduli spaceM. of conformal structures on a compact surface of genus. > 1 together with its Weil- Petersson metric gWP. Our main result is that gWP admits a complete polyhomogeneous expansion in powers of the lengths of the short geodesics up to the singular divisors of the Deligne- Mumford compactification ofM.