New results on the geometry of the moduli space of Riemann surfaces

DOI10.1007/s11425-008-0063-6zbMath1152.14013OpenAlexW2164594151WikidataQ125724165 ScholiaQ125724165MaRDI QIDQ943412

Xiaofeng Sun, Shing Tung Yau, Ke Feng Liu

Publication date: 9 September 2008

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-008-0063-6

zbMATH Keywords

\(L^2\)-cohomology groupMumford goodness of several canonical metrics on the moduli spaces of Riemann surfacesthe perturbed Ricci metric and the Kaehler-Einstein metricthe Ricci metricthe Weil-Petersson metric

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Complex-analytic moduli problems (32G13) Algebraic moduli problems, moduli of vector bundles (14D20) Singularities of curves, local rings (14H20)

Related Items (1)

Metrics on complex manifolds

Cites Work

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• Riemann's mapping theorem for variable metrics
• Canonical metrics on the moduli space of Riemann surfaces. II
• The hyperbolic metric and the geometry of the universal curve
• Chern forms and the Riemann tensor for the moduli space of curves
• Harmonic maps of the moduli space of compact Riemann surfaces
• Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• Hirzebruch's proportionality theorem in the non-compact case
• The irreducibility of the space of curves of a given genus
• Canonical metrics on the moduli space of Riemann surfaces. I

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