On the number and location of short geodesics in moduli space

Christopher J. Leininger, Dan Margalit

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article numberjts025
Pages (from-to)30-48
Number of pages19
JournalJournal of Topology
Issue number1
StatePublished - Mar 2013
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


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