The first eigenvalue of Dirac and Laplace operators on surfaces
| dc.creator | Grosjean, Jean-Francois | |
| dc.creator | Humbert, Emmanuel | |
| dc.date | 2006-09-18 | |
| dc.date.accessioned | 2026-07-07T07:39:43Z | |
| dc.date.available | 2026-07-07T07:39:43Z | |
| dc.description | Let $(M,g,σ)$ be a compact Riemmannian surface equipped with a spin structure $σ$. For any metric $\tilde{g}$ on $M$, we denote by $μ\_1(\tilde{g})$ (resp. $λ\_1(\tilde{g})$) the first positive eigenvalue of the Laplacian (resp. the Dirac operator) with respect to the metric $\tilde{g}$. In this paper, we show that $$\inf \frac{λ\_1(\tilde{g})^2}{μ\_1(\tilde{g})} \leqslant {1/2}.$$ where the infimum is taken over the metrics $\tilde{g}$ conformal to $g$. This answer a question asked by Agricola, Ammann and Friedrich | |
| dc.identifier | https://arxiv.org/abs/math/0609493 | |
| dc.identifier | http://arxiv.org/abs/math/0609493 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121558 | |
| dc.subject | Differential Geometry | |
| dc.subject | 34L15 53C27 58J05 | |
| dc.title | The first eigenvalue of Dirac and Laplace operators on surfaces | |
| dc.type | text |