Holomorphic factorization of determinants of Laplacians using quasi-Fuchsian uniformization

DOI10.1007/s11005-007-0204-9zbMath1154.30035arXivmath/0605605OpenAlexW3104355808MaRDI QIDQ2476621

Lee-Peng Teo, Andrew McIntyre

Publication date: 12 March 2008

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605605

zbMATH Keywords

Teichmüller spaceLaplace-Beltrami operatorSelberg zeta functiondifferentialsregularized determinantLiouville action function

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Teichmüller theory for Riemann surfaces (30F60) Differentials on Riemann surfaces (30F30)

Related Items (7)

Chern-Simons line bundle on Teichmüller space ⋮ Averaging over Narain moduli space ⋮ Holomorphic extensions of Laplacians and their determinants ⋮ Symplectic geometry of the moduli space of projective structures in homological coordinates ⋮ Semiclassical 3D gravity as an average of large-\(c\) CFTs ⋮ Universal index theorem on \(\mathrm{M\"ob}(S^1)\setminus \mathrm{Diff}_+(S^1)\) ⋮ Deligne pairings and families of rank one local systems on algebraic curves

Cites Work

• Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker's first limit formula
• Chern forms and the Riemann tensor for the moduli space of curves
• On determinants of Laplacians on Riemann surfaces
• Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography
• A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces
• The multiplier-series of a Schottky group
• A non-standard integral equation with applications to quasi-conformal mappings
• Some remarks on Teichmüller's space of Riemann surfaces
• Curvature properties of Teichmüller's space
• On spaces of Kleinian groups
• Finite dimensional Teichmüller spaces and generalizations
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