Geometry & Topology

Recurrent Weil–Petersson geodesic rays with non-uniquely ergodic ending laminations

Jeffrey Brock and Babak Modami

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Abstract

We construct Weil–Petersson geodesic rays with minimal filling non-uniquely ergodic ending lamination which are recurrent to a compact subset of the moduli space of Riemann surfaces. This construction shows that an analogue of Masur’s criterion for Teichmüller geodesics does not hold for Weil–Petersson geodesics.

Article information

Source
Geom. Topol., Volume 19, Number 6 (2015), 3565-3601.

Dates
Received: 21 September 2014
Accepted: 6 April 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858881

Digital Object Identifier
doi:10.2140/gt.2015.19.3565

Mathematical Reviews number (MathSciNet)
MR3447110

Zentralblatt MATH identifier
1332.30067

Subjects
Primary: 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

Keywords
Teichmüller space Weil–Petersson metric recurrent geodesics non-uniquely ergodic lamination

Citation

Brock, Jeffrey; Modami, Babak. Recurrent Weil–Petersson geodesic rays with non-uniquely ergodic ending laminations. Geom. Topol. 19 (2015), no. 6, 3565--3601. doi:10.2140/gt.2015.19.3565. https://projecteuclid.org/euclid.gt/1510858881


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