Some applications of collapsing with bounded curvature
| dc.creator | Petrunin, Anton | |
| dc.date | 2003-04-18 | |
| dc.date.accessioned | 2026-07-07T04:57:03Z | |
| dc.date.available | 2026-07-07T04:57:03Z | |
| dc.description | In my talk I will discuss the following results which were obtained in joint work with Wilderich Tuschmann. 1. For any given numbers $m$, $C$ and $D$, the class of $m$-dimensional simply connected closed smooth manifolds with finite second homotopy groups which admit a Riemannian metric with sectional curvature $\vert K \vert\le C$ and diameter $\le D$ contains only finitely many diffeomorphism types. 2. Given any $m$ and any $δ>0$, there exists a positive constant $i_0=i_0(m,δ)>0$ such that the injectivity radius of any simply connected compact $m$-dimensional Riemannian manifold with finite second homotopy group and Ricci curvature $Ric\geδ$, $K\le 1$, is bounded from below by $i_0(m,δ)$. I also intend to discuss Riemannian megafolds, a generalized notion of Riemannian manifolds, and their use and usefulness in the proof of these results. | |
| dc.identifier | https://arxiv.org/abs/math/0304266 | |
| dc.identifier | http://arxiv.org/abs/math/0304266 | |
| dc.identifier | Proceedings of the ICM, Beijing 2002, vol. 2, 315--322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67140 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C | |
| dc.title | Some applications of collapsing with bounded curvature | |
| dc.type | text |