Local Cut Points and Metric Measure Spaces with Ricci Curvature Bounded Below
نویسنده
چکیده
A local cut point is by definition a point that disconnects its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a metric measure space satisfying the generalized Bishop–Gromov inequality. As a corollary, we obtain an upper bound for the number of ends of such a space. We also obtain some obstruction conditions for the existence of a local cut point in a metric measure space satisfying the Bishop–Gromov inequality or the Poincaré inequality. For example, the measured Gromov–Hausdorff limits of Riemannian manifolds with a lower Ricci curvature bound satisfy these two inequalities.
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