Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

In Section 4, as illustrations of the effectiveness and practicability of our L p transference principle, several new L p Brunn-Minkowski type inequalities are established, which

Like many other central objects of interest in convex geometry, such as the L p affine and geominimal surface areas and the L p John ellipsoids (see e.g., [27, 34, 37, 42, 43, 52,

Finally, a very general Minkowski-type inequality, involving two Orlicz functions, two convex bodies, and a star body, is proved, that includes as special cases several others in

(It turns out, mainly as a consequence of results obtained in [15], that Orlicz addition is not associative unless it is already L p addition.) These authors also provide a

alors le corps étoilé K doit être Bp pour un p > 0 (à quelques transforma- tions élémentaires près) et les mesures sont essentiellement celles que

A technical element of this proof that we believe of independent interest is the Poincaré-type trace inequality on convex sets proved in Section 2, with a constant having

Le théorème suivant montre que les seules fonctions f pour lesquelles on a l’égalité dans 2.4.0 sont celles qui sont constantes sur chacun des hyper- plans orthogonaux

In the second part of the paper, we show that every metric measure space satisfying the classical Brunn-Minkowski inequality can be approximated by discrete metric spaces with