Volume, diameter and the minimal mass of a stationary 1-cycle
| dc.creator | Nabutovsky, Alexander | |
| dc.creator | Rotman, Regina | |
| dc.date | 2002-01-28 | |
| dc.date | 2002-10-21 | |
| dc.date.accessioned | 2026-07-07T04:46:09Z | |
| dc.date.available | 2026-07-07T04:46:09Z | |
| dc.description | In this paper we present upper bounds on the minimal mass of a non-trivial stationary 1-cycle. The results that we obtain are valid for all closed Riemannian manifolds. The first result is that the minimal mass of a stationary 1-cycle on a closed n-dimensional Riemannian manifold M^n is bounded from above by (n+2)!d/3, where d is the diameter of a manifold M^n. The second result is that the minimal mass of a stationary 1-cycle on a closed Riemannian manifold M^n is bounded from above by 2(n+2)!Fill Rad(M^n) and, as a corollary, by 2(n+2)!(n+1)n^n(n!)^{1/2}(vol(M^n))^{1/n}, where Fill Rad(M^n) is the filling radius of the manifold, and vol(M^n) is its volume. | |
| dc.description | 35 pages; 1 Figure | |
| dc.identifier | https://arxiv.org/abs/math/0201269 | |
| dc.identifier | http://arxiv.org/abs/math/0201269 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63218 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | Primary: 53C22, 53C23; Secondary: 49Q20 | |
| dc.title | Volume, diameter and the minimal mass of a stationary 1-cycle | |
| dc.type | text |