Hofer-Zehnder capacity and length minimizing paths in the Hofer norm
| dc.creator | Slimowitz, Jennifer | |
| dc.date | 1999-05-18 | |
| dc.date.accessioned | 2026-07-07T05:29:07Z | |
| dc.date.available | 2026-07-07T05:29:07Z | |
| dc.description | We use the criteria of Lalonde and McDuff to determine a new class of examples of length minimizing paths in the group $Ham(M)$. For a compact symplectic manifold $M$ of dimension two or four, we show that a path in $Ham(M)$, generated by an autonomous Hamiltonian and starting at the identity, which induces no non-constant closed trajectories of points in $M$, is length minimizing among homotopic paths. The major step in the proof involves determining an upper bound for the Hofer-Zehnder capacity for symplectic manifolds of the type $(M \times D(a))$ where $M$ is compact and has dimension two or four. In the appendix, we give an alternate proof of Polterovich's result that rotation in $CP^2$ and in the blow-up of $CP^2$ at one point is a length minimizing path with respect to the Hofer norm. Here we use the Gromov capacity and describe the necessary ball embeddings. | |
| dc.description | 34 pages, LaTeX2e, 9 figures. Submitted to Transactions of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/9905105 | |
| dc.identifier | http://arxiv.org/abs/math/9905105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78515 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C15 (Primary); 58F05, 58D05, 58B20 (Secondary) | |
| dc.title | Hofer-Zehnder capacity and length minimizing paths in the Hofer norm | |
| dc.type | text |