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

@article{Leininger2013LimitSO, title={Limit sets of Teichm\"uller geodesics with minimal non-uniquely ergodic vertical foliation}, author={Christopher J. Leininger and Anna Lenzhen and Kasra Rafi}, journal={arXiv: Geometric Topology}, year={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 of the Teichm\"uller geodesic. The construction depends on various parameters, and we show that one can adjust the parameters to ensure that the set of accumulation points of such a geodesic in the Thurston boundary is exactly the set of all possible measured foliations in the homotopy class of…

## 23 Citations

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…

Limits of Teichmüller geodesics in the Universal Teichmüller space

- Mathematics
- 2015

A Thurston boundary of the universal Teichmüller space T(D) is the set of projective bounded measured laminations PMLbdd(D) of D . We prove that each Teichmüller geodesic ray in T(D) converges to a…

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-…

A Thurston boundary and visual sphere of the universal Teichmüller space

- MathematicsJournal d'Analyse Mathématique
- 2021

A Thurston boundary of the universal Teichmuller space T(ⅅ) is the space PMLbdd(ⅅ) of projective bounded measured laminations of ⅅ. A geodesic ray in T(ⅅ) is of generalized Teichmuller-type if it…

Limits in 𝒫ℳℱ of Teichmüller geodesics

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019

In this paper we consider the limit set in Thurston’s compactification{\mathcal{P}\kern-2.27622pt\mathcal{M}\kern-0.284528pt\mathcal{F}}of Teichmüller space of some Teichmüller geodesics defined by…

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…

Exotic limit sets of Teichmüller geodesics in the HHS boundary

- MathematicsGroups, Geometry, and Dynamics
- 2019

We answer a question of Durham, Hagen, and Sisto, proving that a Teichmuller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary 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…

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…

Visual sphere and Thurston's boundary of the Universal Teichm\"uller space

- Mathematics
- 2015

Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{D})$ is the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of $\mathbb{D}$. A geodesic ray in…

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