Symmetrizations

In this chapter we present the operation of symmetrization of sets and briefly touch on the strictly connected operation of rearrangement of functions. We define the main known symmetrizations and, for each of them, we describe its main properties. We also define an abstract setting for dealing with symmetrizations and we present some characterizations of Minkowski and Steiner symmetrizations and of polarization in terms of their properties. We also present shadow systems, and the topic of convergence of successive symmetrals.