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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 ...
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...
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...
Mixed Non-Expansive and Potentially Expansive Properties of a Class of Self-Maps in Metric Spaces
contractive maps non-expansive maps metric space fixed points
2010/12/15
This paper investigates self-maps T : X X which satisfy a distance constraint in a metric
space which mixed point-dependent non-expansive properties, or in particular contractive ones, and p...