This is an announcement for the paper "Convergence in shape of Steiner symmetrizations" by Gabriele Bianchi, Almut Burchard, Paolo Gronchi, and Aljosa Volcic.

Abstract: There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examples show that Steiner symmetrization along a sequence of directions whose differences are square summable does not generally converge. (Note that this may happen even with sequences of directions which are dense in S^{n-1}.) Here we show that such sequences converge in shape. The limit need not be an ellipsoid or even a convex set. We also deal with uniformly distributed sequences of directions, and with a recent result of Klain on Steiner symmetrization along sequences chosen from a finite set of directions.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 52A40 (Primary) 28A75, 11K06, 26D15 (Secondary)

Remarks: 11 pages

Submitted from: gabriele.bianchi@unifi.it

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1206.2041

or

http://arXiv.org/abs/1206.2041