Corpus ID: 231741212

# A Metric Stability Result for the Very Strict CD Condition

```@inproceedings{Magnabosco2021AMS,
title={A Metric Stability Result for the Very Strict CD Condition},
author={Mattia Magnabosco},
year={2021}
}```
In [15] Schultz generalized the work of Rajala and Sturm [13], proving that a weak nonbranching condition holds in the more general setting of very strict CD spaces. Anyway, similar to what happens for the strong CD condition, the very strict CD condition seems not to be stable with respect to the measured Gromov Hausdorff convergence (cf. [11]). In this article I prove a stability result for the very strict CD condition, assuming some metric requirements on the converging sequence and on the… Expand
1 Citations
Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below
• Mathematics
• 2021
In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of aExpand

#### References

SHOWING 1-10 OF 25 REFERENCES
Example of an Highly Branching CD Space
In [3] Ketterer and Rajala showed an example of metric measure space, satisfying the measure contraction property MCP(0, 3), that has different topological dimensions at different regions of theExpand
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
• Mathematics
• 2015
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that forExpand
Equivalent definitions of very strict \$CD(K,N)\$ -spaces
We show the equivalence of the definitions of very strict \$CD(K,N)\$ -condition defined, on one hand, using (only) the entropy functionals, and on the other, the full displacement convexity classExpand
Metric measure spaces with Riemannian Ricci curvature bounded from below
• Mathematics
• 2014
In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out FinslerExpand
NON-BRANCHING GEODESICS AND OPTIMAL MAPS IN STRONG CD(K,∞)-SPACES
We prove that in metric measure spaces where the entropy functional is Kconvex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite secondExpand
Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure
• Mathematics
• 2015
In prior work (4) of the first two authors with Savare, a new Riemannian notion of lower bound for Ricci curvature in the class of metric measure spaces (X,d,m) was introduced, and the correspondingExpand
Ricci curvature for metric-measure spaces via optimal transport
• Mathematics
• 2004
We dene a notion of a measured length space X having nonnegative N-Ricci curvature, for N 2 [1;1), or having1-Ricci curvature bounded below byK, forK2 R. The denitions are in terms of theExpand
Failure of the local-to-global property for CD(K,N) spaces
Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this property is a suitableExpand
On one-dimensionality of metric measure spaces
In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutelyExpand
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Mathematics
• 2014
This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces \$(X,\mathsf {d},\mathfrak {m})\$. Our main results are: A generalExpand