Curvature and rank of Teichmuller space

DOI10.1353/ajm.2006.0003zbMath1092.32008arXivmath/0109045OpenAlexW2079620288MaRDI QIDQ3377741

Benson Farb, Jeffrey F. Brock

Publication date: 29 March 2006

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0109045

zbMATH Keywords

negative sectional curvatureWeil-Petersson metric on Teichmüller spaceGromov-hyperbolic metric

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Local differential geometry of Hermitian and Kählerian structures (53B35) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Teichmüller theory for Riemann surfaces (30F60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (32)

The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores ⋮ Constructing convex planes in the pants complex ⋮ Curve Complexes Versus Tits Buildings: Structures and Applications ⋮ Asymptotic geometry of the mapping class group and Teichmüller space ⋮ Hierarchy paths in the Hatcher-Thurston complex ⋮ Thickness and relative hyperbolicity for graphs of multicurves ⋮ Hyperbolicity of the genus two Hatcher-Thurston complex. ⋮ The asymptotic cone of Teichmüller space and thickness ⋮ The augmented marking complex of a surface ⋮ The genus of curve, pants and flip graphs ⋮ Uniform convergence in the mapping class group ⋮ Optimal Lipschitz maps on one-holed tori and the Thurston metric theory of Teichmüller space ⋮ The Weil-Petersson curvature operator on the universal Teichmüller space ⋮ Translation lengths of parabolic isometries of CAT(0) spaces and their applications ⋮ Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups. ⋮ Geometry of the augmented disk graph ⋮ Hyperbolic quasi-geodesics in CAT(0) spaces. ⋮ Hyperbolicity of the genus two separating curve complex ⋮ Contracting boundaries of CAT(0) spaces ⋮ Geodesic axes in the pants complex of the five-holed sphere ⋮ Semigroup action on \(\mathbb T^n\) ⋮ Asymptotic flatness of the Weil-Petersson metric on Teichmüller space ⋮ Asymptotics of Weil-Petersson geodesics. II: Bounded geometry and unbounded entropy ⋮ A note on Riemannian metrics on the moduli space of Riemann surfaces ⋮ Products of Farey graphs are totally geodesic in the pants graph ⋮ Quasiflats in hierarchically hyperbolic spaces ⋮ Coarse and synthetic Weil-Petersson geometry: Quasi-flats, geodesics and relative hyperbolicity ⋮ Convex cocompact subgroups of mapping class groups ⋮ Stable Teichmüller quasigeodesics and ending laminations ⋮ Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity. ⋮ Large-scale rank and rigidity of the Weil-Petersson metric ⋮ Hyperbolic relatively hyperbolic graphs and disk graphs

This page was built for publication: Curvature and rank of Teichmuller space