Corpus ID: 231741427

Example of an Highly Branching CD Space

@inproceedings{Magnabosco2021ExampleOA,
  title={Example of an Highly Branching CD Space},
  author={Mattia Magnabosco},
  year={2021}
}
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 the space. In this article I propose a refinement of that example, which satisfies the CD(0,∞) condition, proving the non-constancy of topological dimension for CD spaces. This example also shows that the weak curvature dimension bound, in the sense of Lott-SturmVillani, is not sufficient to deduce any… Expand

Figures from this paper

A Metric Stability Result for the Very Strict CD Condition
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 happensExpand

References

SHOWING 1-10 OF 14 REFERENCES
Failure of Topological Rigidity Results for the Measure Contraction Property
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first oneExpand
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
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
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
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
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
Ricci curvature for metric-measure spaces via optimal transport
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 the geometry of metric measure spaces. II
AbstractWe introduce a curvature-dimension condition CD (K, N) for metric measure spaces. It is more restrictive than the curvature bound $\underline{{{\text{Curv}}}} {\left( {M,{\text{d}},m}Expand
Gradient Flows: In Metric Spaces and in the Space of Probability Measures
Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the ConvergenceExpand
On the geometry of metric measure spaces
AbstractWe introduce and analyze lower (Ricci) curvature bounds $ \underline{{Curv}} {\left( {M,d,m} \right)} $ ⩾ K for metric measure spaces $ {\left( {M,d,m} \right)} $. Our definition is based onExpand
...
1
2
...