Asymptotics of the Weil-Petersson metric

2015/03/09 by Rafe Mazzeo, Mazzeo, Rafe, Jan Swoboda +1
Mathematics · #30F10 #32G15 #58D27 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:30F10 #msc:32G15 #msc:58D27

paper · pdf · doi:10.48550/arxiv.1503.02365

31 pages

arxiv created 2015/03/09 · arxiv updated 2015/03/10

Abstract

We consider the Riemann moduli space \mathcal M_γ of conformal structures on a compact surface of genus γ>1 together with its Weil-Petersson metric g_WP. Our main result is that g_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_γ.

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