Results 1 to 10 of about 300,261 (100)
Distance Geometry in Quasihypermetric Spaces. III [PDF]
, 2008 Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by \[ I(\mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y), \] and set $M(X) = \sup I(\mu ...
Nickolas, Peter, Wolf, Reinhard
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Some remarks on the visual angle metric [PDF]
, 2015 We show that the visual angle metric and the triangular ratio metric are comparable in convex domains. We also find the extremal points for the visual angle metric in the half space and in the ball by use of a construction based on hyperbolic geometry ...
Hariri, Parisa +2 more
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Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces [PDF]
, 2016 Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces $\tau_{r,m}$ minimally immersed in spheres to a three-parametric family $T_{a,b,c}$ of tori and Klein bottles ...
Causley, Broderick
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Non-rigidity of spherical inversive distance circle packings [PDF]
, 2011 We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.Comment: 6 pages, one ...
A.V. Pogorelov +9 more
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On Asymptotic Assouad-Nagata Dimension [PDF]
, 2006 For a large class of metric space X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension $\dim(\nu_L X)$ of the Higson corona of X with respect to the sublinear coarse ...
Dranishnikov, A. N., Smith, J.
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, 2017 This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its ...
B. H. BOWDITCH +7 more
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Finite Quasihypermetric Spaces
, 2009 Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by $I(mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y)$, and set $M(X) = \sup I(mu)$, where ...
Nickolas, Peter, Wolf, Reinhard
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Clifford algebra and the projective model of homogeneous metric spaces: Foundations [PDF]
, 2013 This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to physicists and
Sokolov, Andrey
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Geometric Ruzsa triangle inequality in metric spaces with dilations [PDF]
, 2016 The Appendix of the article arXiv:1212.5056 [math.CO] "On growth in an abstract plane" by Nick Gill, H. A. Helfgott, Misha Rudnev, contains a general "geometric Ruzsa triangle inequality" in a Desarguesian projective plane. The purpose of this note is to
Buliga, Marius
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A New Algorithm in Geometry of Numbers
, 2007 A lattice Delaunay polytope P is called perfect if its Delaunay sphere is the only ellipsoid circumscribed about P. We present a new algorithm for finding perfect Delaunay polytopes.
Dutour, Mathieu, Rybnikov, Konstantin
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