Steiner symmetrization, one of the simplest and most powerful symmetrization processes ever introduced in analysis, is a classical and very well-known device, which has seen a number of remarkable applications to problems of geometric and functional nature. Its importance stems from the fact that, besides preserving Lebesgue measure, it acts monotonically on several geometric and analytic quantities associated with subsets of Rn. Among these, perimeter certainly holds a prominent position. Actually, the proof of the isoperimetric property of the ball was the original motivation for Steiner to introduce his symmetrization in.
