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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 20, 2016

Characterization of Low Dimensional RCD*(K, N) Spaces

  • Yu Kitabeppu and Sajjad Lakzian

Abstract

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.

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Received: 2016-5-12
Accepted: 2016-7-21
Published Online: 2016-9-20

© 2016 Yu Kitabeppu and Sajjad Lakzian

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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