2011/10/28 by Christopher J. Leininger, Dan Margalit · 8 citations
Mathematics · #Bounding overwatch #Combinatorics #Computer science #Genus #Geodesic #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Infinity #Intersection (aeronautics) #Mathematical analysis #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Riemann hypothesis #Riemann surface #Space (punctuation) #math.DS #math.GT
paper · pdf · doi:10.1112/jtopol/jts025
published in Journal of Topology 6(1), 30-48 (Wiley) · 23 pages, 1 figure
arxiv created 2011/10/28 · openalex publication_date 2012/11/14 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A closed Teichmüller geodesic in the moduli space ℳg of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that, for any L>0, there exist R>ϵ>0, independent of g, so that the L-short geodesics in ℳg all lie in the intersection of the ϵ-thick part and the R-thin part. We also estimate the number of L-short geodesics in ℳg, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.