Geometry & Topology

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

Jeffrey Brock and Babak Modami

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.)

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


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.

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