# Prescribing the behavior of Weil-Petersson geodesics in the moduli space of Riemann surfaces

@article{Modami2012PrescribingTB, title={Prescribing the behavior of Weil-Petersson geodesics in the moduli space of Riemann surfaces}, author={Babak Modami}, journal={arXiv: Geometric Topology}, year={2012} }

We study Weil-Petersson (WP) geodesics with narrow end invariant and develop techniques to control length-functions and twist parameters along them and prescribe their itinerary in the moduli space of Riemann surfaces. This class of geodesics is rich enough to provide for examples of closed WP geodesics in the thin part of the moduli space, as well as divergent WP geodesic rays with minimal filling ending lamination.
Some ingredients of independent interest are the following: A strength…

## 11 Citations

### Asymptotics of a class of Weil-Petersson geodesics and divergence of WP geodesics

- Mathematics
- 2014

We show that the strong asymptotic class of Weil-Petersson (WP) geodesics with narrow end invariant, [Mod15], and bounded annular coefficients is determined by the forward ending lamination. This…

### Limit sets of Weil-Petersson geodesics

- Mathematics
- 2016

In this paper we prove that the limit set of any Weil-Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichm\"uller space. On the…

### Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II

- Mathematics
- 2016

Abstract Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is…

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

- Mathematics
- 2014

We construct Weil-Petersson (WP) 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…

### MINIMAL NONUNIQUELY ERGODIC VERTICAL FOLIATION, II

- Mathematics
- 2016

Given a sequence of curves on a surface, we provide con- ditions which ensure that (1) the sequence is an innite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is repre-…

### Limit sets of Teichm\"uller geodesics with minimal non-uniquely ergodic vertical foliation

- Mathematics
- 2013

We describe a method for constructing Teichm\"uller geodesics where the vertical measured foliation $\nu$ is minimal but is not uniquely ergodic and where we have a good understanding of the behavior…

### On the geometry of the Thurston metric on Teichmüller spaces : geodesics that disobey an analogue of Masur ’ s criterion

- Mathematics
- 2021

We construct a counterexample for an analogue of Masur’s criterion in the setting of Teichmüller space with the Thurston metric. For that, we find a minimal, filling, non-uniquely ergodic lamination…

### Limit sets of Weil–Petersson geodesics with nonminimal ending laminations

- MathematicsJournal of Topology and Analysis
- 2018

In this paper, we construct examples of Weil–Petersson geodesics with nonminimal ending laminations which have [Formula: see text]-dimensional limit sets in the Thurston compactification of…

### Masur's criterion does not hold in Thurston metric

- Mathematics
- 2019

We construct a counterexample for Masur's criterion in the setting of Teichm\"uller space with Thurston metric. For that, we find a minimal, non-uniquely ergodic lamination $\lambda$ on a seven-times…

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