Results 51 to 60 of about 5,510,773 (262)
Hyperbolicity in Teichmüller space [PDF]
Geometry & Topology, 2014 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.
openaire +4 more sources
The Half-Space Model of Pseudo-hyperbolic Space
, 2022 24 pages, 6 figures. Added Lemma 6.2 and additional details in the proofs of Propositions 2.5 and 5.1; other minor improvements and ...
Seppi A., Trebeschi E.
openaire +2 more sources
, 2016 We consider a `contracting boundary' of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space.
Cashen, Christopher H.
core +2 more sources
Boundaries of hyperbolic metric spaces [PDF]
Pacific Journal of Mathematics, 2005 We investigate the relationship between the metric boundary and the Gromov boundary of a hyperbolic metric space. We show that the Gromov boundary is a quotient topological space of the metric boundary, and that therefore a word-hyperbolic group has an amenable action on the metric boundary of its Cayley graph.
Webster, Corran, Winchester, Adam
openaire +3 more sources
What is a hierarchically hyperbolic space? [PDF]
Beyond Hyperbolicity, 2017 The first part of this survey is a heuristic, non-technical discussion of what an HHS is, and the aim is to provide a good mental picture both to those actively doing research on HHSs and to those who only seek a basic understanding out of pure curiosity.
A. Sisto
semanticscholar +1 more source
Real‐World Performance of CSF Kappa Free Light Chains in the 2024 McDonald Criteria
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Kappa free light chains (KFLCs) in the cerebrospinal fluid (CSF) have a similar performance to CSF‐restricted oligoclonal bands (OCB) for multiple sclerosis (MS) diagnosis. To help with implementation, we set out to resolve several remaining uncertainties: (1) performance in a real‐world cohort and the 2024 McDonald criteria; (2 ...
Maya M. Leibowitz +11 more
wiley +1 more source
Geodesics in Trees of Hyperbolic and Relatively Hyperbolic Spaces [PDF]
Proceedings of the Edinburgh Mathematical Society, 2015 AbstractWe present a careful approximation of the quasi-geodesics of trees of hyperbolic and relatively hyperbolic spaces. As an application we prove a dynamical and geometric combination theorem for trees of relatively hyperbolic spaces, with both Farb's and Gromov's definitions.
openaire +2 more sources
Ball Packings in Hyperbolic Space
, 2023 In hyperbolic space density cannot be defined by a limit as we define it in Euclidean space. We describe the local density bounds for sphere packings and we discuss the different attempts to define optimal arrangements in hyperbolic space.
Tóth, Gábor Fejes +2 more
openaire +2 more sources
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective To investigate the value of constructing models based on habitat radiomics and pathomics for predicting the risk of progression in high‐grade gliomas. Methods This study conducted a retrospective analysis of preoperative magnetic resonance (MR) images and pathological sections from 72 patients diagnosed with high‐grade gliomas (52 ...
Yuchen Zhu +14 more
wiley +1 more source
Journal of Humanistic Mathematics, 2013 We discuss how a creature accustomed to Euclidean space would fare in a world of hyperbolic or spherical geometry, and conversely. Various optical illusions and counterintuitive experiences arise, which can be explicated mathematically using plane models of these geometries.
openaire +4 more sources