 |
|
|
|
| HAL: hal-00002414, version 2 |
| arXiv: math.DG/0407530 |
| Detailed view |  Export this paper |
|
|
| Available versions: | v1 (2004-07-30) | v2 (2004-11-29) |
|
|
|
|
| Extremality for the Vafa-Witten bound on the sphere |
|
|
| Marc Herzlich 1 |
|
|
| (2004-07-30) |
|
|
|
| We prove that the round metric on the sphere has the largest first eigenvalue of the Dirac operator among all metrics that are larger than it. As a corollary, this gives an alternative proof of an extremality result for scalar curvature due to M. Llarull. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
|
|
|
CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc |
|
|
|
|
|
|
|
|
|
| Subject | : | Mathematics/Differential Geometry |
|
|
| Dirac operator – eigenvalue estimate – scalar curvature. |
|
|
|
|
|
| hal-00002414, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00002414 | |
| oai:hal.archives-ouvertes.fr:hal-00002414 | |
| From: Marc Herzlich | |
| Submitted on: Monday, 29 November 2004 15:52:03 | |
| Updated on: Monday, 29 November 2004 16:13:56 | |
