2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222745On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.26 pagesDifferential Geometry53A30, 53C27 (Primary), 58J50, 58C40 (Secondary)text