Extremality for the Vafa-Witten bound on the sphere

Marc Herzlich (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: Dirac operator; eigenvalue estimate; scalar curvature.; scalar curvature

Domaines: Géométrie différentielle [math.DG]

Marc Herzlich. Extremality for the Vafa-Witten bound on the sphere. Geometric And Functional Analysis, 2005, 15, pp.1153-1161. ⟨10.1007/s00039-005-0536-5⟩. ⟨hal-00002414v2⟩