Results 11 to 20 of about 510,591 (285)
The Binet-Legendre Metric in Finsler Geometry [PDF]
Geometry & Topology, 2012 For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions.
Bao +30 more
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Metrics for Probabilistic Geometries [PDF]
CoRR, 2014 We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is given by a Gaussian ...
Tosi, Alessandra +3 more
openaire +4 more sources
Metric geometry of spaces of persistence diagrams. [PDF]
J Appl Comput TopolAbstractPersistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a family of functors $${\mathcal {D}}_p$$ D p
Che M +3 more
europepmc +5 more sources
Canonical differential geometry of string backgrounds [PDF]
, 2006 String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field.
A. Fotopoulos +15 more
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The Gromov–Wasserstein Distance: A Brief Overview
Axioms, 2014 We recall the construction of the Gromov–Wasserstein distance and concentrate on quantitative aspects of the definition.
Facundo Mémoli
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The Dual Gromov-Hausdorff Propinquity [PDF]
, 2014 Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*-algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named ...
Alfsen +45 more
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Geometry of the Cassinian Metric and Its Inner Metric [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2015 12 ...
Ibragimov, Zair +3 more
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Algebroids, AKSZ Constructions and Doubled Geometry
Complex Manifolds, 2021 We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop the theory of ...
Marotta Vincenzo Emilio +1 more
doaj +1 more source
Area metric gravity and accelerating cosmology [PDF]
, 2006 Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop in detail the
+33 more
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COARSE AND FINE GEOMETRY OF THE THURSTON METRIC
Forum of Mathematics, Sigma, 2020 We study the geometry of the Thurston metric on the Teichmüller space of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type; however, we focus particular ...
DAVID DUMAS +3 more
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