Geodesic
Characterization of Low Dimensional RCD*(K, N) Spaces
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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}},
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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/