Convergence in shape of Steiner symmetrizations Gabriele BianchiAlmut BurchardPaolo GronchiAljosa Volcic Primary 52A40Secondary 28A7511K0626D15Steiner symmetrization It is known that the iterated Steiner symmetrals of any given compact sets converge to a ball for most sequences of directions. However, examples show that Steiner symmetrization along a sequence of directions whose differences are square summable does not generally converge. Here we show that such sequences converge \emph{in shape}. The limit need not be an ellipsoid or even a convex set. We also consider uniformly distributed sequences of directions, and we extend a recent result of Klain on Steiner symmetrization along sequences chosen from a finite set of directions. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.5087 10.1512/iumj.2012.61.5087 en Indiana Univ. Math. J. 61 (2012) 1695 - 1710 state-of-the-art mathematics http://iumj.org/access/