26 citations · 54 across the 12 of their papers we have counts for
12 papers
Teichmüller disks with small limit sets in PMF
Anna Lenzhen
We study limit sets of Teichmüller disks in the Thurston boundary of Teichmüller space of a closed surface S of genus at least 2. It is well known that almost every Teichmüller geo…
Thurston geodesics: no backtracking and active intervals
Anna Lenzhen, Babak Modami, Kasra Rafi +1
We develop the notion of the active interval for a subsurface along a geodesic in the Thurston metric on Teichmuller space of a surface S. That is, for any geodesic in the Thurston…
Cyclic hyperbolic Veech groups in finite area
Anna Lenzhen, Juan Souto
We prove that there are finite area flat surfaces whose Veech group is an infinite cyclic group consisting of hyperbolic elements
Coarse and fine geometry of the Thurston metric
David Dumas, Anna Lenzhen, Kasra Rafi +1
We study the geometry of the Thurston metric on the Teichmüller space of hyperbolic structures on a surface . Some of our results on the coarse geometry of this…
Teichmueller geodesics with d-dimensional limit sets
Anna Lenzhen, Babak Modami, Kasra Rafi
We construct an example of a Teichmueller geodesic ray whose limit set in Thurston boundary of Teichmueller space is a d-dimensional simplex.
Variations on a Theorem of Birman and Series
Anna Lenzhen, Juan Souto
Suppose that is a hyperbolic surface and a monotonic function. We study the closure in the projective tangent bundle of the set of all geode…
The shadow of a Thurston geodesic to the curve graph
Anna Lenzhen, Kasra Rafi, Jing Tao
We study the geometry of the Thurston metric on Teichmuller space by examining its geodesics and comparing them to Teichmuller geodesics. We show that, similar to a Teichmuller geo…
Bounded combinatorics and the Lipschitz metric on Teichmüller space
Anna Lenzhen, Kasra Rafi, Jing Tao
Considering the Teichmüller space of a surface equipped with Thurston's Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these…
New solutions to the Hurwitz problem on square identities
Anna Lenzhen, Sophie Morier-Genoud, Valentin Ovsienko
The Hurwitz problem of composition of quadratic forms, or of "sum of squares identity" is tackled with the help of a particular class of -graded non-associative a…
Length of a curve is quasi-convex along a Teichmuller geodesic
Anna Lenzhen, Kasra Rafi
We show that for every simple closed curve α, the extremal length and the hyperbolic length of αare quasi-convex functions along any Teichmuller geodesic. As a corollary, we conclu…
Divergence of Teichmueller Geodesics
Anna Lenzhen, Howard Masur
We study the asymptotic geometry of Teichmueller geodesic rays. We show that when the transverse measures to the vertical foliations of the quadratic differentials determining two…
Teichmuller geodesics that do not have a limit in PMF
Anna Lenzhen
We construct a Teichmuller geodesic which does not have a limit on the Thurston boundary of the Teichmuller space.