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Journal of Convex Analysis 17 (2010), No. 1, 035--049
Copyright Heldermann Verlag 2010

Functional Inequalities Derived from the Brunn--Minkowski Inequalities for Quermassintegrals

Andrea Colesanti
Dip. di Matematica 'U. Dini', Università di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy

Eugenia Saorín Gómez
Dep. de Matematicas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain

We 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.

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