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Almost‐isometry between Teichmüller metric and length‐spectrum metric on moduli space
Author(s) -
Liu L.,
Su W.
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdr052
Subject(s) - mathematics , metric (unit) , isometry (riemannian geometry) , pure mathematics , metric space , isometric exercise , teichmüller space , injective metric space , spectrum (functional analysis) , moduli space , metric differential , mathematical analysis , cone (formal languages) , space (punctuation) , fisher information metric , convex metric space , intrinsic metric , physics , computer science , algorithm , operations management , quantum mechanics , economics , medicine , operating system , physical therapy , riemann surface
We prove an analogue of Farb–Masur's theorem that the length‐spectrum metric on moduli space is ‘almost isometric’ to a simple model ( S ) which is induced by the cone metric over the complex of curves. As an application, we know that the Teichmüller metric and the length‐spectrum metric are ‘almost isometric’ on moduli space, while they are not even quasi‐isometric on Teichmüller space.