Results 21 to 30 of about 620,022 (302)
PTOLEMAIC SPACES AND CAT(0) [PDF]
Glasgow Mathematical Journal, 2009 AbstractWe consider Ptolemy's inequality in a metric space setting. It is not hard to see that CAT(0) spaces satisfy this inequality. Although the converse is not true in full generality, we show that if our Ptolemaic space is either a Riemannian or Finsler manifold, then it must also be CAT(0).
Buckley, Stephen M. +2 more
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Conformal deformations of CAT(0) spaces [PDF]
Mathematische Annalen, 2018 We show that the class of CAT(0) spaces is closed under suitable conformal changes. In particular, any CAT(0) space admits a large variety of non-trivial deformations.
Alexander Lytchak, Stephan Stadler
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New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space
مجلة بغداد للعلوم, 2021 Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact
Ahmed Jameel Kadhim
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A quadratic rate of asymptotic regularity for CAT(0)-spaces
Journal of Mathematical Analysis and Applications, 2005 In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results guarantee only exponential bounds. The method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a ...
Laurenţiu Leuştean
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The configuration space of a robotic arm in a tunnel of width 2 [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We study the motion of a robotic arm inside a rectangular tunnel of width 2. We prove that the configuration space S of all possible positions of the robot is a CAT(0) cubical complex.
Federico Ardila +3 more
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On Approximating Fixed Point in CAT(0) Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, we obtain a new modified iteration process in the setting of CAT(0) spaces involving generalized $\alpha$-nonexpansive mapping. We prove strong and $\Delta$ convergence results for approximating fixed point via newly defined iteration ...
Chanchal Garodia, Izhar Uddin
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On the geodesic flow on CAT(0) spaces [PDF]
Ergodic Theory and Dynamical Systems, 2019 Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen–Margulis’ measure finiteness assumption used by Ricks [Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces. Ergod. Th. & Dynam. Sys. 37 (2017), 939–970] is removed.
Ioannis Papadoperakis +2 more
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An Intrinsic Characterization of Five Points in a CAT(0) Space
Analysis and Geometry in Metric Spaces, 2020 Gromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov.
Toyoda Tetsu
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Bulletin of the Belgian Mathematical Society - Simon Stevin, 2017 We extend the Gromov geometric definition of CAT(0) spaces to the case where the comparison triangles are not in the Euclidean plane but belong to a general Banach space. In particular, we study the case where the Banach space is $\ell_p$, for $p > 2$.
Khamsi, M. A., Shukri, S. A.
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On the Halpern iteration in CAT(0) spaces [PDF]
Annals of Functional Analysis, 2015 In this paper, strong convergence of Halpern iteration is shown for a quasi-strongly nonexpansive sequence of multivalued mappings in complete CAT(0) spaces.
Khatibzadeh, Hadi, Ranjbar, Sajad
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