2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159675We use Brunn-Minkowski inequalities for quermassintegrals to deduce a family of inequalities of Poincaré type on the unit sphere and on the boundary of smooth convex bodies in the $n$-dimensional Euclidean space.15 pagesFunctional AnalysisMetric Geometry52A20; 26D10text