Collapsing Manifolds with Boundary
| dc.creator | Wong, Jeremy | |
| dc.date | 2007-11-21 | |
| dc.date.accessioned | 2026-07-07T08:44:29Z | |
| dc.date.available | 2026-07-07T08:44:29Z | |
| dc.description | This manuscript studies manifolds-with-boundary collapsing in the Gromov-Hausdorff topology. The main aim is an understanding of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space, which is presumed to be without geodesic terminals. The main result establishes a disc bundle structure for any manifold-with-boundary having two-sided bounds on sectional curvature and second fundamental form, and a lower bound on intrinsic injectivity radius, which is sufficiently close in the Gromov-Hausdorff topology to a closed manifold. The second main result identifies Gromov-Hausdorff limits of certain sequences of manifolds-with-boundary as Alexandrov spaces of curvature bounded below. | |
| dc.description | 49 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0711.3483 | |
| dc.identifier | http://arxiv.org/abs/0711.3483 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142672 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C (primary), 51K (secondary) | |
| dc.title | Collapsing Manifolds with Boundary | |
| dc.type | text |