Steiner symmetrization $$(n-1)$$(n-1) times is sufficient to transform an ellipsoid to a ball in $${\mathbb {R}}^n$$Rn

In this article, we show that Steiner symmetrization $$(n-1)$$ times is sufficient to transform an ellipsoid to a ball in $${\mathbb {R}}^n$$ . Specifically, we seek out the $$(n-1)$$ directions in the unit sphere such that the destination of the corresponding Steiner symmetrization is the standard ball.