Local cut points and metric measure spaces with Ricci curvature bounded below
| dc.creator | Watanabe, Masayoshi | |
| dc.date | 2006-10-05 | |
| dc.date.accessioned | 2026-07-07T07:28:43Z | |
| dc.date.available | 2026-07-07T07:28:43Z | |
| dc.description | A 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.description | 26 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0610170 | |
| dc.identifier | http://arxiv.org/abs/math/0610170 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117839 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21, 53C23, 31C15 | |
| dc.title | Local cut points and metric measure spaces with Ricci curvature bounded below | |
| dc.type | text |