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math.MG2013★ 1 cited
On the local convexity of intersection bodies of revolution
M. Angeles Alfonseca, Jaegil Kim
One of the fundamental results in Convex Geometry is Busemann's theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is only natural to a…
math.MG2013
An extension of a result by Lonke to intersection bodies
M. A. Alfonseca
In this paper we prove that intersection bodies cannot be direct sums using Fourier analytic techniques. This extends a result by Lonke. We also prove a necessary regularity condit…
math.MG2013
Intersection bodies that are not polar zonoids: A flat top condition in dimensions four and six
M. A. Alfonseca
We find general geometric conditions on a convex body of revolution K, in dimensions four and six, so that its intersection body IK is not a polar zonoid. We exhibit several exampl…