The Velling-Kirillov metric of the universal Teichmüller curve

DOI10.1007/BF02789310zbMath1079.30064arXivmath/0206202OpenAlexW1973000217MaRDI QIDQ2565907

Lee-Peng Teo

Publication date: 28 September 2005

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0206202

zbMATH Keywords

Schwarzian derivativesymplectic formWeil-Petersson metricTeichmüller theoryBers' embeddingKrillov metric

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Teichmüller theory for Riemann surfaces (30F60)

Related Items (14)

Euler-Arnold equations and Teichmüller theory ⋮ Zygmund functions on the real line and quasiconformal deformations ⋮ Universal Teichmüller space and BMO ⋮ Weil-Petersson Teichmüller space revisited ⋮ Fourier coefficients of Zygmund functions and analytic functions with quasiconformal deformation extensions ⋮ Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theory ⋮ Bers isomorphism on the universal Teichmüller curve ⋮ Fiber structure and local coordinates for the Teichmüller space of a bordered Riemann surface ⋮ Universal index theorem on \(\mathrm{M\"ob}(S^1)\setminus \mathrm{Diff}_+(S^1)\) ⋮ On Grunsky operator ⋮ A complex structure on the set of quasiconformally extendible non-overlapping mappings into a Riemann surface ⋮ Conformal mappings and dispersionless Toda hierarchy ⋮ The geometry of the universal Teichmüller space and the Euler-Weil-Petersson equation ⋮ A Hilbert manifold structure on the Weil–Petersson class Teichmüller space of bordered Riemann surfaces

Cites Work

• Diff(S\({}^ 1)\) and the Teichmüller spaces
• Kähler structures on K-orbits of the group of diffeomorphisms of the circle
• Kähler geometry of the infinite-dimensional homogeneous space \(M=Diff_+(S^ 1)/Rot(S^ 1)\)
• Ordinary differential equations and quasiconformal mappings
• A non-standard integral equation with applications to quasi-conformal mappings
• Fiber spaces over Teichmüller spaces
• Quasiconformal reflections
• Symmetric Structures on a Closed Curve
• A lattice‐point problem in hyperbolic space
• On the Tangent Space to the Universal Teichmuller Space
• Uniformization, Moduli, and Kleinian Groups†
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