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三亚国际数学论坛：Curvatures of Graphs,Simplicial Complexes and Metric Spaces（Curvatures of Graphs,Simplicial Complexes and Metric Spaces ）
三亚国际数学论坛 Curvatures of Graphs Simplicial Complexes Metric Spaces
2017/1/10
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...
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Ricci curvature metric measure spaces branching metric spaces Differential Geometry
2012/3/1
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 ...
Common fixed points theorem for two multivalued mappings in cone metric spaces
functional analysis common fixed point non normal cone multivalued mapping cone metric spaces
2011/10/20
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...
Injective hulls of certain discrete metric spaces and groups
Injective hulls certain discrete metric spaces and groups Group Theory
2011/9/23
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 ...
Existence of complete Lyapunov functions for semiflows on separable metric spaces
Lyapunov functions Semiflows Separable metric space
2011/9/23
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...
Local Poincare inequalities from stable curvature conditions on metric spaces
Ricci curvature metric measure spaces geodesics Poincare inequality
2011/9/20
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...
Distance sets of universal and Urysohn metric spaces
Distance sets of universal Urysohn metric spaces Combinatorics
2011/9/20
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 $\mathrm{M}$...
Quadratic estimates for perturbed Dirac type operators on doubling measure metric spaces
Quadratic estimates holomorphic functional calculi doubling measure measure metric space Dirac type operators
2011/9/15
Abstract: We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for...
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...
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...
Subgroups of isometries of Urysohn-Katetov metric spaces of uncountable density
Subgroups of isometries of Urysohn-Katetov metric uncountable density
2011/1/18
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...
Compatibility of type (\alpha) and weak compatibility in fuzzy metric spaces
Fuzzy metric space common fixed points
2010/9/21
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...
Spectral metric spaces for Gibbs measures
Noncommutative Geometry Spectral Triple Entropy Gibbs Measure
2011/2/25
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...