Displaying similar documents to “Angles between Curves in Metric Measure Spaces”

A rough curvature-dimension condition for metric measure spaces

Anca-Iuliana Bonciocat (2014)

Open Mathematics

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We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations...

Characterization of Low Dimensional RCD*(K, N) Spaces

Yu Kitabeppu, Sajjad Lakzian (2016)

Analysis and Geometry in Metric Spaces

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In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking,...

Generalized P-reducible (α,β)-metrics with vanishing S-curvature

A. Tayebi, H. Sadeghi (2015)

Annales Polonici Mathematici

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We study one of the open problems in Finsler geometry presented by Matsumoto-Shimada in 1977, about the existence of a concrete P-reducible metric, i.e. one which is not C-reducible. In order to do this, we study a class of Finsler metrics, called generalized P-reducible metrics, which contains the class of P-reducible metrics. We prove that every generalized P-reducible (α,β)-metric with vanishing S-curvature reduces to a Berwald metric or a C-reducible metric. It follows that there...

Menger curvature and Lipschitz parametrizations in metric spaces

Immo Hahlomaa (2005)

Fundamenta Mathematicae

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We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.

On isotropic Berwald metrics

Akbar Tayebi, Behzad Najafi (2012)

Annales Polonici Mathematici

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We prove that every isotropic Berwald metric of scalar flag curvature is a Randers metric. We study the relation between an isotropic Berwald metric and a Randers metric which are pointwise projectively related. We show that on constant isotropic Berwald manifolds the notions of R-quadratic and stretch metrics are equivalent. Then we prove that every complete generalized Landsberg manifold with isotropic Berwald curvature reduces to a Berwald manifold. Finally, we study C-conformal changes...

On some type of curvature conditions

Mohamed Belkhelfa, Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Dorota Kowalczyk, Leopold Verstraelen (2002)

Banach Center Publications

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In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.

An area formula in metric spaces

Valentino Magnani (2011)

Colloquium Mathematicae

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We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure-theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure". Finally, we give some applications and examples.