This is an announcement for the paper "The geometry of p-convex intersection bodies" by Jaegil Kim, Vladyslav Yaskin and Artem Zvavitch.
Abstract: 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
Archive classification: math.FA
Mathematics Subject Classification: 44A12, 52A15, 52A21
Submitted from: zvavitch@math.kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1006.1546
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