Rare Teichmüller disks converge to small limit sets.
problem Understanding limit sets of Teichmüller disks.
method Analyzing Thurston boundary of Teichmüller space.
result Teichmüller disks with smallest limit sets are exceptional.
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48 results for “Teichmuller”
The study examines the asymptotic behavior of extremal length in Teichmüller space.
problem Understanding the asymptotic behavior of extremal length along Teichmüller rays.
method Analyzing the limit of extremal length and deriving formulas for limiting Teichmüller distance and detour metric.
result An explicit formula for the limiting Teichmüller distance and a necessary and sufficient condition for Teichmüller rays to be asymptotic.
We prove that the every quasi-isometry of Teichmüller space equipped with the Teichmüller metric is a bounded distance from an isometry of Teichmüller space. That is, Teichmüller space is quasi-isometrically rigid.
Study on Teichmüller rays' asymptotic behavior and distances.
problem Understanding the asymptotic behavior of Teichmüller rays.
method Explicit formula derivation for limiting Teichmüller distance under specific conditions.
result Two Teichmüller rays are asymptotic if their vertical measured foliations are modularly equivalent and their limit surfaces coincide.
We prove that the Bergman and the Teichmuller metrics are equivalent on Teichmuller spaces.
We prove that the Teichmüller space of surfaces with given boundary lengths equipped with the arc metric (resp. the Teichmüller metric) is almost isometric to the Teichmüller space of punctured surfaces equipped with the Thurston metric (resp. the Teichmüller metric).
Royden proved that any isometry of Teichmuller space in the Teichmuller metric must be an element of the extended mapping class group M(S). He also proved that the Teichmuller metric is not symmetric at any point. In this paper we give extensions of Royden's theorems from the Teichmuller metric to an arbitrary complete…
We study the Lipschitz metric on Teichmuller space (defined by Thurston) and compare it with the Teichmuller metric. We show that in the thin part of Teichmuller space the Lipschitz metric is approximated up to bounded additive distortion by the sup metric on a product of lower-dimensional spaces (similar to the Teichm…
Classifying complex geodesics for the Carathéodory metric on low-dimensional Teichmüller spacesmath.GT
It was recently shown that the Carathéodory and Teichmüller metrics on the Teichmüller space of a closed surface do not coincide. On the other hand, Kra earlier showed that the metrics coincide when restricted to a Teichmüller disk generated by a differential with no odd-order zeros. Our aim is to classify Teichmüller …
The Teichmüller curve is the fiber space over Teichmüller space of closed Riemann surfaces, where the fiber over a point in Teichmüller space is the underlying surface. We derive formulas for sectional curvatures on the Teichmüller curve. In particular, our method can be applied to investigate the geometry of the Weil-…
Teichmüller space rigidity proven for Thurston metric.
problem Understanding isometries in Teichmüller space with Thurston metric.
method Analyzing -linear surjective isometries between cotangent spaces.
result Every isometry between hyperbolic surfaces induces an isometry in Teichmüller space.
We obtain basic estimates for a Monge-Ampère equation introduced by Moncrief in the study of the Relativistic Teichmüller Theory. We then give another proof of the parametrization of the Teichmüller space obtained by Moncrief. Our approach provides yet another proof of the classical Teichmüller theorem that the Teichmü…
Proves regularity of harmonic maps into Teichmüller space.
problem Harmonic maps into Teichmüller space and their singularities.
method Analyzes harmonic maps from Riemannian domains to Teichmüller space with specific conditions.
result If a harmonic map intersects a stratum, it is entirely contained in that stratum.
Develops second order infinitesimal structures on Teichmüller space.
problem Understand the infinitesimal structures of Teichmüller space.
method Formulated second order infinitesimal structures over Teichmüller space.
result Affirmative answers to two folklore problems on Teichmüller space.
Unique geodesics selected by energy minimization in Teichmüller space.
problem Finding a unique geodesic between points in Teichmüller space.
method Energy minimization of harmonic map rays, extending Thurston boundary.
result Selection of a unique Thurston geodesic through points in Teichmüller space.
Collar parameters for Teichmuller Space & Measured Foliations on a Surface Research Announcementmath.GT
New coordinates for Teichmüller space compactification.
problem Compactification of Teichmüller space.
method Defined new coordinates.
result Thurston compactification is radial compactification of Euclidean space.
Calculates twist in Teichmüller space using cross ratios.
problem Calculating the Fenchel-Nielsen twist in Teichmüller space.
method Using cross ratio coordinates.
result Compact calculation of twist in Teichmüller space.
Busemann points are sparse in Teichmüller spaces.
problem Characterizing the limits of geodesic rays in Teichmüller spaces.
method Proof of nowhere density of Busemann points in horoboundaries.
result Teichmüller metrics lack non-positive curvature.
Extends Teichmüller distance concept to non-distance maps.
problem Defining distance metrics for non-distance functions.
method Generalizes horofunction compactification to non-distance maps.
result Defines horofunction counterpart to Teichmüller distance.
No primitive Teichmüller curves found in Prym(2,2).
problem Existence of primitive Teichmüller curves in Prym(2,2).
method Completed work by Lanneau and Möller.
result No primitive Teichmüller curves in Prym(2,2).
New Teichmüller geodesic rays found with unique foliations.
problem Capturing generic directions in Teichmüller space.
method Using Chaika-Masur-Wolf and Durham-Zalloum work.
result First sublinearly-Morse geodesic rays with minimal non-uniquely ergodic foliations.
Hodge and Teichmüllermath.GT
Derives integral formula for Hodge and Teichmüller norms.
problem Relationship between Hodge and Teichmüller norms.
method Integrals and cohomology classes.
result Comparison between Hodge and Teichmüller norms.
Isometric embeddings of Teichmüller spaces are derived from branched coverings.
problem Characterizing isometric embeddings of Teichmüller spaces.
method Holomorphic isometric embeddings induced by branched coverings.
result All isometric embeddings of Teichmüller spaces of dimension at least 2 arise from branched coverings.
Study of infinity in Teichmüller space using Thurston boundary.
problem Metric structure on Thurston boundary of Teichmüller space.
method Developed tools in sup metrics and applied Minsky's theorem.
result Investigation of metric structure on Thurston boundary.
Given a measured geodesic lamination on a hyperbolic surface, grafting the surface along multiples of the lamination defines a path in Teichmuller space, called the grafting ray. We show that every grafting ray, after reparametrization, is a Teichmuller quasi-geodesic and stays in a bounded neighborhood of a Teichmulle…
We show that the horofunction compactification of Teichmüller space with the Teichmüller metric is homeomorphic to the Gardiner-Masur compactification.
The paper establishes a Poisson integral formula for bounded pluriharmonic functions on Teichmüller space.
problem Analyzing bounded pluriharmonic functions on Teichmüller space.
method Establishing a Poisson integral formula.
result A Poisson integral formula for bounded pluriharmonic functions on Teichmüller space.
Criterion found for Teichmüller extremal maps on infinite Riemann surfaces.
problem Finding necessary and sufficient conditions for Teichmüller extremal maps.
method Established a criterion for Teichmüller-type extremal maps.
result Criterion for Teichmüller extremal maps on infinite Riemann surfaces.
We show that the length spectrum metric on Teichmüller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichmüller space with quasiconformal and the Fenchel-Nielsen Teichmüller spaces on such surfaces
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 conclude that, in Teichmuller space equipped with the Teichmuller metric, balls are quasi- convex.
Random walk speed on Teichmüller space is a proper function.
problem Understanding the speed of random walks on Teichmüller space.
method Adaptation of Gouëzel's pivoting techniques to Teichmüller space.
result Speed of random walk is a proper function on Teichmüller space.
Mapping class group dynamics tracked through Teichmüller space.
problem Tracking mapping class group actions on Teichmüller space.
method Action on Teichmüller space and geometric intersection numbers.
result Effective estimate of mapping class group actions on Teichmüller space.
Researchers confirm a conjecture about metrics on a specific Teichmüller space.
problem Proving the conjecture about metrics on a specific Teichmüller space.
method Analyzing a specific Teichmüller space of genus 2 with 0 punctures.
result The conjecture is confirmed for a specific Teichmüller space.
The Bers-Greenberg theorem tells that the Teichmüller space of a Riemann surface with branch points (orbifold) depends only on the genus and the number of special points, but not on the particular ramification values. On the other hand, the Maskit embedding provides a mapping from the Teichmüller space of an orbifold, …
We construct a Teichmuller geodesic which does not have a limit on the Thurston boundary of the Teichmuller space.
Study on Carathéodory metric discrepancies on Teichmüller spaces.
problem Determine if Carathéodory metric agrees with Teichmüller metric on Teichmüller spaces.
method Analyzed general case of Teichmüller spaces, proving metric discrepancies except for seven specific spaces.
result Proved Carathéodory metric disagrees with Teichmüller metric on all Teichmüller spaces except seven specific ones.
We prove that the Teichmuller Space of Riemann Surfaces of genus g>1, equipped with the Teichmuller metric, is not a Gromov Hyperbolic space.
Paper compares Bergman kernel and Masur-Veech measure on Teichmüller space.
problem Comparing Bergman kernel and Masur-Veech measure on Teichmüller space.
method Comparison between Bergman kernel form and pushforward measure of Masur-Veech measure.
result Obtained a comparison between the Bergman kernel form and the pushforward measure of the Masur-Veech measure.
We extend Weil-Petersson theory to infinite type Teichmüller spaces.
problem Defining and analyzing Weil-Petersson geometry for infinite-dimensional Teichmüller spaces.
method Rigorous definition of complex Hilbert manifold structures, Kähler geometry, and global analysis.
result Generalizations of the period mapping and Weil-Petersson Teichmüller space in other fields.
On the inclusion of the quasiconformal Teichmüller space into the length-spectrum Teichmüller spacemath.GT
Given a surface of infinite topological type, there are several Teichmüller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the comparison between the quasiconformal Teichmüller space and the length-spectrum Teichm…
The paper counts conjugacy classes of pseudo-Anosov homeomorphisms in Teichmüller space.
problem Counting conjugacy classes of pseudo-Anosov homeomorphisms in Teichmüller space.
method Analyzes the asymptotic behavior of conjugacy classes as the radius of a ball in Teichmüller space increases.
result Asymptotics for the number of pseudo-Anosov homeomorphisms conjugate to a given homeomorphism within a ball of radius R centered at X.
We review and organize some results describing the behavior of a Teichmüller geodesic and draw several applications: 1) We show that Teichmüller geodesics do not back track. 2) We show that a Teichmüller geodesic segment whose endpoints are in the thick part has the fellow travelling property. This fails when the endpo…
Unlike the case of surfaces of topologically finite type, there are several different Teichmüller spaces that are associated to a surface of topological infinite type. These Teichmüller spaces first depend (set-theoretically) on whether we work in the hyperbolic category or in the conformal category. They also depend, …
A commentary on Teichmüller's paper "Veränderliche Riemannsche Flächen" (Variable Riemann Surfaces)math.GT
This is a commentary on Teichmüllers' paper "Veränderliche Riemannsche Flächen" (Variable Riemann Surfaces), published in 1944. This paper is the last one that Teichmüller wrote on the problem of moduli. At most places the paper contains ideas and no technical details. The author presents a completely new approach to T…
New map connects stability conditions to Teichmüller space.
problem Stability conditions and Teichmüller space relationship.
method Using harmonic maps and 3-Calabi-Yau categories.
result Natural map between stability conditions and Teichmüller space.
In this paper, we obtain the explicit limit value of the Teichmüller distance between two Teichmüller geodesic rays which are determined by Jenkins-Strebel differentials having a common end point on the augmented Teichmüller space. Furthermore, we also obtain a condition under which these two rays are asymptotic. This …
Harmonic mappings into Teichmuller spaces appear in the study of manifolds which are fibrations whose fibers are Riemann surfaces. In this article we will study the existence and uniquenesses questions of harmonic mappings into Teichmuller spaces, as well as some local and global behavior of the harmonic images induced…
Extends Teichmüller space quasi-isometry to -multicurve graphs.
problem Quasi-isometric relationship between Teichmüller space and curve graphs.
method Electrifying Teichmüller space along thin part, adapting Lackenby-Yazdi pants graph bounds.
result Quasi-isometry of -multicurve graph to electrified Teichmüller space.