Data di Pubblicazione:
2012
Citazione:
Local curvature-dimension condition implies measure-contraction property / F. Cavalletti, K.T. Sturm. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 262:12(2012 Jun 15), pp. 5110-5127. [10.1016/j.jfa.2012.02.015]
Abstract:
We prove that for non-branching metric measure spaces the local curvature condition CD loc(K, N) implies the global version of MCP(K, N). The curvature condition CD(K, N) introduced by the second author and also studied by Lott and Villani is the generalization to metric measure space of lower bounds on Ricci curvature together with upper bounds on the dimension. This paper is the following step of Bacher and Sturm (2010) [1] where it is shown that CD loc(K, N) is equivalent to a global condition CD *(K, N), slightly weaker than the usual CD(K, N). It is worth pointing out that our result implies sharp Bishop-Gromov volume growth inequality and sharp Poincaré inequality.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Metric geometry; Optimal transport; Ricci curvature;
Elenco autori:
F. Cavalletti, K.T. Sturm
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