相关论文: The asymptotic geometry of the Teichm\"uller metri…
We study the asymptotic behavior of extremal length along Teichm\"uller rays. Specifically, we determine the limit of extremal length along a Teichm\"uller ray and obtain an explicit expression for this limit, which complements a related…
In this paper, we consider the asymptotic behavior of two Teichm\"uller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem in \cite{Amano14}. We also consider the infimum of the asymptotic…
In this paper, we study the limit of Teichm\"uller distance between two points along a pair of Teichm\"uller rays. We obtain an explicit formula for the limiting Teichm\"uller distance when the vertical measured foliations of the quadratic…
The Gardiner-Masur compactification of Teichm\"uller space is homeomorphic to the horofunction compactification of the Teichm\"uller metric. Let $\xi$ and $\eta$ be a pair of boundary points in the Gardiner-Masur compactification that fill…
We prove that the set of Busemann points (the limits of almost-geodesic rays) is nowhere dense in the horoboundary of the Teichm\"uller metric for all Teichm\"uller spaces of complex dimension strictly larger than 1. This shows that the…
We show that any grafting ray in Teichm\"{u}ller space is (strongly) asymptotic to some Teichm\"{u}ller geodesic ray. As an intermediate step we introduce surfaces that arise as limits of these degenerating Riemann surfaces. Given a…
In this paper, we give a framework for the study of the extremal length geometry of Teichm\"uller space after S. Kerckhoff, F. Gardiner and H. Masur. There is a natural compactification using extremal length geometry introduced by Gardiner…
We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the Teichm\"uller metric is approximated up…
We give an example of a horocycle in the Teichm\"uller space of the five-times-punctured sphere that does not converge in the Gardiner--Masur compactification, or equivalently in the horofunction compactification of the Teichm\"uller…
In this paper, we obtain the explicit limit value of the Teichm\"{u}ller distance between two Teichm\"{u}ller geodesic rays which are determined by Jenkins-Strebel differentials having a common end point on the augmented Teichm\"{u}ller…
In this paper, we shall show that the metric boundary of the Teichmueller space with respect to the Teichmueller distance contains non-Busemann points when the complex dimension of the Teichmueller space is at least two.
The Teichm\"uller space $\mathcal{T}(\Sigma)$ of a surface $\Sigma$ is equipped with Thurston's asymmetric metric. Stretch lines are oriented geodesics for this metric on $\mathcal{T}(\Sigma)$. We give the asymptotic behavior of the lengths…
In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmuller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this…
We provide a geometric condition which determines whether or not every point on the metric boundary of a graph with the standard path metric is a Busemann point, that is it is the limit point of a geodesic ray. We apply this and a related…
Considering the Teichm\"uller space of a surface equipped with Thurston's Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and that the closest-point…
Given a measure on the Thurston boundary of Teichmueller space, one can pick a geodesic ray joining some basepoint to a randomly chosen point on the boundary. Different choices of measures may yield typical geodesics with different…
Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{H})$ is the set of asymptotic rays to the embedding of $T(\mathbb{H})$ in the space of geodesic currents; the boundary is identified with the projective bounded measured…
In this paper, we introduce a new asymmetric weak metric on the Teichm{\"u}ller space of a closed orientable surface with (possibly empty) punctures.This new metric, which we call the Teichm{\"u}ller-Randers metric, is an asymmetric…
We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary finite-dimensional bounded convex domain D. We determine its set of Busemann points, which are those points that are the limits of `almost-geodesics'.…
We show that any grafting ray in Teichm\"{u}ller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichm\"{u}ller geodesic ray. As a consequence the projection of a generic grafting ray to moduli…