On the measure contraction property of metric measure spaces | Zendy

Shinichi Ohta | Zendy

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On the measure contraction property of metric measure spaces

Author(s) -

Shinichi Ohta

Publication year - 2007

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/110

Subject(s) - mathematics , ricci curvature , contraction (grammar) , measure (data warehouse) , hausdorff measure , pure mathematics , scalar curvature , curvature of riemannian manifolds , riemannian geometry , mathematical analysis , hausdorff distance , curvature , sectional curvature , hausdorff dimension , geometry , medicine , computer science , database

We introduce a measure contraction property of metric measure spaces which can be regarded as a generalized notion of the lower Ricci curvature bound on Riemannian manifolds. It is actually equivalent to the lower bound of the Ricci curvature in the Riemannian case. We will generalize the Bonnet?Myers theorem, and prove that this property is preserved under the measured Gromov?Hausdorff convergence.

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