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Curvature is a notion originally developed in differential and Riemannian geometry. It was then discovered that curvature inequalities in Riemannian manifolds are equivalent to other geometric propert...
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy ...
In this paper, a new generalized contractive condition is introduced in metric space. By the condition and without the normality of the cone, the existence of common fixed points of multivalued mappin...
Abstract: Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. Isbell showed that every metric space X has an injective hull E(X). We prove that ...
Abstract: The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the exis...
Abstract: We prove local Poincar\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is...
Abstract: A metric space $\mathrm{M}=(M;\de)$ is {\em homogeneous} if for every isometry $f$ of a finite subspace of $\mathrm{M}$ to a subspace of $\mathrm{M}$ there exists an isometry of $\mathrm{M}$...
Abstract: This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhausti...
Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of to...
The magnitude of metric spaces      magnitude  metric spaces        2011/2/28
Magnitude is a real-valued invariant of metric spaces, analogous to the Euler characteristic of topological spaces and the cardinality of sets. The de nition of magnitude is a special case of a gener...
According to Katˇetov (1988), for every infinite cardinal m satisfying m n ≤ m for all n < m, there exists a unique m-homogeneous universal metric space Um of weight m.
A metric space is a set M together with a real-valued function d(x, y)defined for x, y ∈ M that satisfies the following three conditions. First,d(x, y) ≥ 0 for every x, y ∈ M, and d(x, y) = 0 if and o...
The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a contractive condition of [8] through compatibility of type (α) and weak compatibility wi...
We construct spectral metric spaces for Gibbs measures on a onesided topologically exact subshift of finite type. That is, for a given Gibbs measure we construct a spectral triple and show that Connes...
We are interested in studying doubling metric spaces with the property that at some of the points the metric tangent is unique. In such a setting, Finsler-Carnot-Carath&acute;eodory geometries and Car...

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