On the measure contraction property of metric measure spaces 论文
2007Commentarii Mathematici Helvetici引用 249顶会
Geometric Analysis and Curvature FlowsTopological and Geometric Data AnalysisAdvanced Neuroimaging Techniques and Applications
摘要
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.