arXiv Analytics

Sign in

arXiv:1207.7286 [math.MG]AbstractReferencesReviewsResources

Rotation invariant Minkowski classes of convex bodies

Rolf Schneider, Franz E. Schuster

Published 2012-07-31Version 1

A Minkowski class is a closed subset of the space of convex bodies in Euclidean space Rn which is closed under Minkowski addition and non-negative dilatations. A convex body in Rn is universal if the expansion of its support function in spherical harmonics contains non-zero harmonics of all orders. If K is universal, then a dense class of convex bodies M has the following property. There exist convex bodies T1; T2 such that M + T1 = T2, and T1; T2 belong to the rotation invariant Minkowski class generated by K. It is shown that every convex body K which is not centrally symmetric has a linear image, arbitrarily close to K, which is universal. A modified version of the result holds for centrally symmetric convex bodies. In this way, a result of S. Alesker is strengthened, and at the same time given a more elementary proof.

Related articles: Most relevant | Search more
arXiv:1403.1643 [math.MG] (Published 2014-03-07, updated 2014-04-24)
New Orlicz Affine Isoperimetric Inequalities
arXiv:1604.05351 [math.MG] (Published 2016-04-12)
On the volume of sections of a convex body by cones
arXiv:math/9201204 [math.MG] (Published 1989-10-26)
Shadows of convex bodies