Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space

DOI10.4171/CMH/336zbMath1323.35119arXiv1206.4010MaRDI QIDQ484258

Yong-Cai Geng, Sumit K. Garg

Publication date: 6 January 2015

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.4010

zbMATH Keywords

moduli spacespectral theoryRiemann surfaceWeil-Petersson metricWeyl law

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Spectrum, resolvent (47A10) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15)

Related Items (2)

Riemann moduli spaces are quantum ergodic ⋮ Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces

Cites Work

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• The Weil-Petersson geodesic flow is ergodic
• Growth of the Weil-Petersson diameter of moduli space
• Spectral geometry of singular Riemannian spaces
• Behavior of geodesic-length functions on Teichmüller space
• Good geometry on the curve moduli
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• On the geometry of Weil-Petersson completion of Teichmüller spaces
• Asymptotic expansion of the heat kernel for orbifolds
• The signature package on Witt spaces
• Geometry of Algebraic Curves
• Families of Riemann surfaces and Weil-Petersson geometry
• Understanding Weil-Petersson curvature

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