We show that the horoboundary of outer space for the Lipschitz metric is a quotient of Culler and Morgan's classical boundary, two trees being identified whenever their translation length functions are homothetic in restriction to the set of primitive elements of . We identify the set of Busemann points with the s…
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8 results for “horoboundaries”
The horoboundary of Teichmüller space is path connected and has non-dense Busemann points.
problem Characterizing the horoboundary of Teichmüller space.
method Using the relationship between the horofunction and visual compactifications of Teichmüller spaces.
result The horoboundary of Teichmüller space is path connected and has non-dense Busemann points.
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.
The paper is devoted to the large scale geometry of the Heisenberg group equipped with left-invariant Riemannian distances. We prove that two such distances have bounded difference if and only if they are asymptotic, i.e., their ratio goes to one, at infinity. Moreover, we show that for every left-invariant…
We show that the horofunction boundary of Teichmüller space with Thurston's Lipschitz metric is the same as the Thurston boundary. We use this to determine the isometry group of the Lipschitz metric, apart from in some exceptional cases. We also show that the Teichmüller spaces of different surfaces, when endowed with …
New metric on geodesic currents connects different surface genera.
problem Understanding geodesic currents on surfaces of varying genera.
method Introducing a new asymmetric metric on the space of projective filling geodesic currents.
result Metric spaces of projective filling geodesic currents for surfaces of different genera are not isometric.
Two trees in the boundary of outer space are said to be \emph{primitive-equivalent} whenever their translation length functions are equal in restriction to the set of primitive elements of . We give an explicit description of this equivalence relation, showing in particular that it is nontrivial. This question is …
We prove central limit theorems for the random walks on either the mapping class group of a closed, connected, orientable, hyperbolic surface, or on , each time under a finite second moment condition on the measure (either with respect to the Teichmüller metric, or with respect to the Lipschitz metric …