Extremal metric for the first eigenvalue on a Klein bottle
| dc.creator | Jakobson, Dmitry | |
| dc.creator | Nadirashvili, Nikolai | |
| dc.creator | Polterovich, Iosif | |
| dc.date | 2003-11-26 | |
| dc.date | 2005-12-10 | |
| dc.date.accessioned | 2026-07-07T06:35:49Z | |
| dc.date.available | 2026-07-07T06:35:49Z | |
| dc.description | The first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called extremal metrics. The only known extremal metrics are a round sphere, a standard projective plane, a Clifford torus and an equilateral torus. We construct an extremal metric on a Klein bottle. It is a metric of revolution, admitting a minimal isometric embedding into a 4-sphere by the first eigenfunctions. Also, this Klein bottle is a bipolar surface for the Lawson's {3,1}-torus. We conjecture that an extremal metric for the first eigenvalue on a Klein bottle is unique, and hence it provides a sharp upper bound for the first eigenvalue on a Klein bottle of a given area. We present numerical evidence and prove the first results towards this conjecture. | |
| dc.description | 20 pages; minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0311484 | |
| dc.identifier | http://arxiv.org/abs/math/0311484 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99911 | |
| dc.subject | Spectral Theory | |
| dc.subject | Differential Geometry | |
| dc.subject | 58E11, 58J50, 53C21 | |
| dc.title | Extremal metric for the first eigenvalue on a Klein bottle | |
| dc.type | text |