Results 11 to 20 of about 332 (52)
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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Geometry without topology as a new conception of geometry
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 12, Page 733-760, 2002., 2002 A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T‐geometric one are considered. T‐geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian ...
Yuri A. Rylov
wiley +1 more source
Gluing Hyperconvex Metric Spaces
Analysis and Geometry in Metric Spaces, 2015 We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along ...
Miesch Benjamin
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Chordal Hausdorff Convergence and Quasihyperbolic Distance
Analysis and Geometry in Metric Spaces, 2020 We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).
Herron David A. +2 more
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Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature
Analysis and Geometry in Metric Spaces, 2019 We prove distance bounds for graphs possessing positive Bakry-Émery curvature apart from an exceptional set, where the curvature is allowed to be non-positive.
Liu Shiping +3 more
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Embeddings of locally finite metric spaces into Banach spaces
, 2007 We show that if X is a Banach space without cotype, then every locally finite metric space embeds metrically into X.Comment: 6 pages, to appear in Proceedings of the ...
Baudier, Florent, Lancien, Gilles
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Sharp distortion growth for bilipschitz extension of planar maps
, 2012 This note addresses the quantitative aspect of the bilipschitz extension problem. The main result states that any bilipschitz embedding of $\mathbb R$ into $\mathbb R^2$ can be extended to a bilipschitz self-map of $\mathbb R^2$ with a linear bound on ...
Kovalev, Leonid V.
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On a general matrix-valued unbalanced optimal transport problem
European Journal of Applied MathematicsWe introduce a general class of transport distances $\mathrm {WB}_{\Lambda }$ over the space of positive semi-definite matrix-valued Radon measures $\mathcal {M}(\Omega, \mathbb {S}_+^n)$ , called the weighted Wasserstein–Bures distance ...
Bowen Li, Jun Zou
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Classifying homogeneous ultrametric spaces up to coarse equivalence
, 2019 For every metric space $X$ we introduce two cardinal characteristics $\mathrm{cov}^\flat(X)$ and $\mathrm{cov}^\sharp(X)$ describing the capacity of balls in $X$.
Banakh, Taras, Repovš, Dušan
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Some applications of Ball's extension theorem [PDF]
, 2006 We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type 2 problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an ...
Mendel, Manor, Naor, Assaf
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