Results 1 to 10 of about 791 (17)
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
core +1 more source
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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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
core +4 more sources
The isometries of the cut, metric and hypermetric cones [PDF]
, 2003 We show that the symmetry groups of the cut cone Cut(n) and the metric cone Met(n) both consist of the isometries induced by the permutations on {1,...,n}; that is, Is(Cut(n))=Is(Met(n))=Sym(n) for n>4. For n=4 we have Is(Cut(4))=Is(Met(4))=Sym(3)xSym(4).
Deza, Antoine +2 more
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On the Hausdorff volume in sub-Riemannian geometry [PDF]
, 2011 For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous
A. Agrachev +30 more
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Combinatorial problems of (quasi-)crystallography
, 2002 Several combinatorial problems of (quasi-)crystallography are reviewed with special emphasis on a unified approach, valid for both crystals and quasicrystals. In particular, we consider planar sublattices, similarity sublattices, coincidence sublattices,
Baake, Michael, Grimm, Uwe
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Buildings have finite asymptotic dimension
, 2007 In this note, we show that the asymptotic dimension of any building is finite and equal to the asymptotic dimension of an apartment in that building.Comment: 4 pages; v2: typos corrected, to appear in Russian Journal of Mathematical Physics, special ...
Dymara, Jan, Schick, Thomas
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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
core
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
core
Coincidence site modules in 3-space
, 2006 The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, by using maximal orders in quaternion algebras of class number 1 over ...
Baake, Michael +2 more
core +2 more sources