1998/01/07 by Feng Luo
Mathematics · #math.GT #msc:57
published as J. Differential Geometry, Vol. 48, 1998, 275-317. · 32 pages, 13 figures
arxiv created 1998/01/07 · arxiv updated 2009/11/30
Given a compact orientable surface with finitely many punctures Σ, let \Cal S(Σ) be the set of isotopy classes of essential unoriented simple closed curves in Σ. We determine a complete set of relations for a function from \Cal S(Σ) to \bold R to be the geodesic length function of a hyperbolic metric with geodesic boundary and cusp ends on Σ. As a conse quence, the Teichmüller space of hyperbolic metrics with geodesic boundary and cusp ends on Σ is reconstructed from an intrinsic (\bold QP1, PSL(2, \bold Z)) structure on \Cal S(Σ).