Geodesic
Characterization of Low Dimensional RCD*(K, N) Spaces
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1
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In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking, a converse to the Lévy-Gromov’s isoperimetric inequality and was previously only known for Ricci limit spaces) which might be also of independent interest.
Mots-clés : Low dimensional, metric measure spaces, Riemannian Ricci curvature bound, curvaturedimension, Bishop-Gromov, Ahlfors regular, Ricci limit spaces 
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     author = {Kitabeppu, Yu and Lakzian, Sajjad},
     title = {Characterization of {Low} {Dimensional} {RCD*(K,} {N)} {Spaces}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2016},
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     number = {1},
     zbl = {1348.53046},
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Kitabeppu, Yu; Lakzian, Sajjad. Characterization of Low Dimensional RCD*(K, N) Spaces. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a7/