Herzlich, M. Extremality for the Vafa-Witten bound on the sphere. (English) Zbl 1137.53334 Geom. Funct. Anal. 15, No. 6, 1153-1161 (2005). Summary: 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. Cited in 4 Documents MSC: 53C27 Spin and Spin\({}^c\) geometry 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 58C40 Spectral theory; eigenvalue problems on manifolds PDF BibTeX XML Cite \textit{M. Herzlich}, Geom. Funct. Anal. 15, No. 6, 1153--1161 (2005; Zbl 1137.53334) Full Text: DOI arXiv OpenURL