On the Finsler structure of Teichmüller's metric and Thurston's metric

DOI10.1016/j.exmath.2013.12.007zbMath1308.32017arXiv1111.4079OpenAlexW1844158102MaRDI QIDQ2258855

WeiXu Su, Athanase Papadopoulos

Publication date: 27 February 2015

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4079

zbMATH Keywords

Teichmüller spaceThurston's asymmetric metricFinsler normTeichmüller's metric

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) General geometric structures on low-dimensional manifolds (57M50) Teichmüller theory for Riemann surfaces (30F60)

Related Items

A differential formula of extremal length and its applications, Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes, A divergent horocycle in the horofunction compactification of the Teichmüller metric, The Finsler geometry of the Teichmüller metric, Local rigidity of the Teichmüller space with the Thurston metric, Systolic surfaces of arithmetic hyperbolic 3-manifolds, Extremal length functions are log-plurisubharmonic, Equidistribution of families of expanding horospheres on moduli spaces of hyperbolic surfaces, Quasi-Fuchsian Co-Minkowski Manifolds

Cites Work

• Bounded combinatorics and the Lipschitz metric on Teichmüller space
• Unification of extremal length geometry on Teichmüller space via intersection number
• Quadratic differentials and foliations
• Length spectra and the Teichmüller metric for surfaces with boundary
• Measured foliations and the minimal norm property for quadratic differentials
• Teichmüller rays and the Gardiner-Masur boundary of Teichmüller space
• On elementary antistretch lines
• Moduli of graphs and automorphisms of free groups
• The asymptotic geometry of Teichmüller space
• The length spectra as moduli for compact Riemann surfaces
• On Thurston's boundary of Teichmüller space and the extension of earthquakes
• Schiffer's interior variation and quasiconformal mapping
• The moduli space of Riemann surfaces is Kähler hyperbolic
• The diameter of the thick part of moduli space and simultaneous Whitehead moves
• Shift coordinates, stretch lines and polyhedral structures for Teichmüller space
• Confromal invariants and function-theoretic null-sets
• Almost-isometry between Teichmüller metric and length-spectrum metric on moduli space
• On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary
• The horoboundary and isometry group of Thurston's Lipschitz metric
• The horofunction compactification of Teichm\"uller metric
• On the classification of mapping class actions on Thurston's asymmetric metric
• Comparison between Teichmüller and Lipschitz metrics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item