The Dual Brunn-Minkowski Inequalities for Intersection Bodies and Two Additions

Abstract

In this paper, some dual Brunn-Minkowski inequalities are established for intersection bodies for the harmonic Blaschke additions and p-radial additions.

Brunn-Minkowski inequalities for star duals of intersection bodies and two additions

“…with equality if and only if K is a dilation of L. Proof For u ∈ S n−1 , according to (8), (9) and the Minkowski integral inequality, we have…”

“…The intersection body was introduced in 1988 by Lutwak, who found a close connection between these bodies and the well-known 1956 Busemann-Petty problem asking whether origin symmetric convex bodies with larger central hyperplane sections also have greater volume. Some results regarding the intersection body can be found in [8][9][11][12][13][14][15]. The projection bodies have been an object of intense investigation during the past three decades.…”