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.
@article{bwmeta1.element.doi-10_1515_agms-2016-0007,
author = {Yu Kitabeppu and Sajjad Lakzian},
title = {Characterization of Low Dimensional RCD*(K, N) Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {4},
year = {2016},
zbl = {1348.53046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0007}
}
Yu Kitabeppu; Sajjad Lakzian. Characterization of Low Dimensional RCD*(K, N) Spaces. Analysis and Geometry in Metric Spaces, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0007/