The geometry of p-convex intersection bodies

Details The geometry of p-convex intersection bodies The geometry of p-convex intersection bodies

2010-06-08

arxiv.org/abs/1006.1546v2

Mathematics

Functional Analysis

Scientific paper

Busemann's theorem states that the intersection body of an origin-symmetric convex body is also convex. In this paper we provide a version of Busemann's theorem for p-convex bodies. We show that the intersection body of a p-convex body is q-convex for certain q. Furthermore, we discuss the sharpness of the previous result by constructing an appropriate example. This example is also used to show that IK, the intersection body of K, can be much farther away from the Euclidean ball than K. Finally, we extend these theorems to some general measure spaces with log-concave and $s$-concave measures

Affiliated with

Also associated with

No associations

Rating

The geometry of p-convex intersection bodies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The geometry of p-convex intersection bodies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The geometry of p-convex intersection bodies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-30186