Stability of metric measure spaces with integral Ricci curvature bounds
TLDR
In this article, it was shown that a sequence of n-dimensional Riemannian manifolds subconverges to a metric measure space that satisfies the curvature-dimension condition C D ( K, n ) in the sense of Lott-Sturm-Villani provided the L p -norm for p > n 2 of the part of the Ricci curvature that lies below K converges to 0.About:
This article is published in Journal of Functional Analysis.The article was published on 2021-10-15 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Ricci curvature & Curvature.read more
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Limits of manifolds with a Kato bound on the Ricci curvature
TL;DR: In this paper, the structure of Gromov-Hausdorff limits of sequences of Riemannian manifolds whose Ricci curvature satisfies a uniform Kato bound was studied.
Almost maximal volume entropy rigidity for integral Ricci curvature in the non-collapsing case
TL;DR: In this article , the authors show the almost maximal volume entropy rigidity for manifolds with lower integral Ricci curvature bound in the noncollapsing case, where the curvatures of the manifolds are assumed to be smooth.
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Non-Hilbertian tangents to Hilbertian spaces
TL;DR: In this paper , the authors provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not in fact infinitely Hilbertian.
Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound
Liang Chen,Shicheng Xu +1 more
TL;DR: For Riemannian n -manifolds with a negative lower Ricci curvature bound and a upper diameter bound, it was known that almost maximal volume entropy admits if and only if it is diffeomorphic and Gromov-Hausdor close to a hyperbolic space form as mentioned in this paper .
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Non-Hilbertian tangents to Hilbertian spaces
TL;DR: In this paper, the authors provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric spaces having pmGH-tangents that are not infinite-immediately Hilbertian.
References
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Book
Optimal Transport: Old and New
TL;DR: In this paper, the authors provide a detailed description of the basic properties of optimal transport, including cyclical monotonicity and Kantorovich duality, and three examples of coupling techniques.
Book
A Course in Metric Geometry
TL;DR: In this article, a large-scale Geometry Spaces of Curvature Bounded Above Spaces of Bounded Curvatures Bounded Below Bibliography Index is presented. But it is based on the Riemannian metric space.
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On the geometry of metric measure spaces. II
TL;DR: In this article, a curvature-dimension condition CD(K, N) for metric measure spaces is introduced, which is more restrictive than the curvature bound for Riemannian manifolds.
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Ricci curvature for metric-measure spaces via optimal transport
John Lott,Cédric Villani +1 more
TL;DR: In this paper, a notion of a length space X having nonnegative N-Ricci curvature, for N 2 [1;1], or having 1-RICci curvatures bounded below by K, for K2 R, was given.