Local cut points and metric measure spaces with Ricci curvature bounded below

dc.creatorWatanabe, Masayoshi
dc.date2006-10-05
dc.date.accessioned2026-07-07T07:28:43Z
dc.date.available2026-07-07T07:28:43Z
dc.descriptionA local cut point is by definition a point that disconnectes 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.
dc.description26 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/0610170
dc.identifierhttp://arxiv.org/abs/math/0610170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117839
dc.subjectDifferential Geometry
dc.subject53C21, 53C23, 31C15
dc.titleLocal cut points and metric measure spaces with Ricci curvature bounded below
dc.typetext

Files

Collections