Results 61 to 70 of about 17,194 (132)
A characterization of hyperbolic spaces
, 2006 We show that a geodesic metric space, and in particular the Cayley graph of a finitely generated group, is hyperbolic in the sense of Gromov if and only if intersections of any two metric balls balls is itself "almost" a metric ball.
Chatterji, Indira, Niblo, Graham A.
core
An obstruction to the strong relative hyperbolicity of a group
, 2006 We give a simple combinatorial criterion for a group that, when satisfied, implies the group cannot be strongly relatively hyperbolic. Our criterion applies to several classes of groups, such as surface mapping class groups, Torelli groups, and ...
Javier Aramayona +5 more
core +1 more source
Limits of cubic differentials and buildings
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In the Labourie–Loftin parameterization of the Hitchin component of surface group representations into SL(3,R)$\mathrm{SL}(3,\mathbb {R})$, we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that ray.
John Loftin +2 more
wiley +1 more source
A characterization of hyperbolic spaces
, 2007 We show that a geodesic metric space, and in particular the Cayley graph of a finitely generated group, is hyperbolic in the sense of Gromov if and only if intersections of any two metric balls balls is itself "almost" a metric ball.
Chatterji, Indira, Niblo, Graham A.
core
Uniformity from Gromov hyperbolicity
Illinois Journal of Mathematics, 2008 The authors show that, in a metric space \(X\) with annular convexity, the uniform domains are precisely those Gromov hyperbolic domains whose quasiconformal structure on the boundary agrees with that on the boundary of \(X\). As an application it is shown that quasi-Möbius maps between geodesic spaces with annular convexity preserve uniform domains ...
Herron, David +2 more
openaire +3 more sources
The geometry of the disk complex [PDF]
, 2013 We give a distance estimate for the disk complex. We use the distance estimate to prove that the disk complex is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting,
Schleimer, Saul, Masur, Howard
core +1 more source
A characterization of Gromov hyperbolicity of surfaces with variable negative curvature
, 2021 In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature K≤ −k² < 0, we just need to verify the Rips condition on a very small class of triangles, namely, those contained in simple closed geodesics. This result is,
Tourís, Eva, Portilla, Ana
core
Stability of Gromov hyperbolicity [PDF]
, 2009 20 pages, 1 figure.-- MSC2000 codes: 30F45; 53C23, 30C99.Zbl#: Zbl pre05652685A main problem when studying any mathematical property is to determine its stability, i.e., under what type of perturbations it is preserved.
Tourís, Eva +2 more
core +2 more sources
Connectivity of the space of ending laminations [PDF]
, 2009 We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E.
Leininger, Christopher J. +1 more
core +1 more source
Relatively dominated representations from eigenvalue gaps and limit maps. [PDF]
Geom Dedic, 2023 Zhu F.
europepmc +1 more source