2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72063We 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.to appear in G.A.F.ADifferential Geometry53C27 ; 58J50 ; 58J60text