A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle
| dc.creator | Soufi, Ahmad El | |
| dc.creator | Giacomini, Hector | |
| dc.creator | Jazar, Mustapha | |
| dc.date | 2007-01-26 | |
| dc.date.accessioned | 2026-07-07T07:43:20Z | |
| dc.date.available | 2026-07-07T07:43:20Z | |
| dc.description | We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich \cite{JNP}: on the Klein bottle $\mathbb{K}$, the metric of revolution $$g_0= {9+ (1+8\cos ^2v)^2\over 1+8\cos ^2v} (du^2 + {dv^2\over 1+8\cos ^2v}),$$ $0\le u <\fracπ2$, $0\le v <π$, is the \emph{unique} extremal metric of the first eigenvalue of the Laplacian viewed as a functional on the space of all Riemannian metrics of given area. The proof leads us to study a Hamiltonian dynamical system which turns out to be completely integrable by quadratures. | |
| dc.identifier | https://arxiv.org/abs/math/0701773 | |
| dc.identifier | http://arxiv.org/abs/math/0701773 | |
| dc.identifier | Duke Mathematical Journal 135(1) (2006) 181--202 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122784 | |
| dc.subject | Metric Geometry | |
| dc.subject | 58J50; 58E11; 35P15 | |
| dc.title | A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle | |
| dc.type | text |