Right-angled billiards and volumes of moduli spaces of quadratic differentials on ℂP1

Jayadev S. Athreya, Alex Eskin, Anton Zorich, Jon Chaika

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We use the relation between the volumes of the strata of meromorphic quadratic differentials with at most simple poles on ℂP1 and counting functions of the number of (bands of) simple closed geodesics in associated flat metrics with singularities to prove a very explicit formula for the volume of each such stratum conjectured by M. Kontsevich a decade ago. Applying ergodic techniques to the Teichmüller geodesic flow we obtain quadratic asymptotics for the number of (bands of) closed trajectories and for the number of generalized diagonals in almost all right-angled billiards.

Original languageEnglish
Pages (from-to)1311-1386
Number of pages76
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume49
Issue number6
Publication statusPublished - 1 Nov 2016
Externally publishedYes

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