Functional inequalities derived from the Brunn-Minkowski inequalities   for quermassintegrals
  We use Brunn-Minkowski inequalities for quermassintegrals to deduce a family of inequalities of Poincar\'e type on the unit sphere and on the boundary of smooth convex bodies in the $n$-dimensional Euclidean space. 
Andrea Colesanti, Eugenia Saorin-Gomez