Extremality for the Vafa-Witten bound on the sphere

2004/07/30 by Marc Herzlich, Herzlich, Marc
Mathematics · #53C27 #58J50 #58J60 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C27 #msc:58J50 #msc:58J60

paper · pdf · doi:10.48550/arxiv.math/0407530

to appear in G.A.F.A

arxiv created 2004/11/29 · arxiv updated 2009/12/01

Abstract

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.

Related

• Vafa-Witten bound on the complex projective space
• Total mean curvature and first Dirac eigenvalue
• Extremal Metric for the First Eigenvalue on a Klein Bottle
• Extremal metric for the first eigenvalue on a Klein bottle
• Dirac eigenvalues and the hyperspherical radius