Đề tài " The perimeter inequality under Steiner symmetrization: Cases of equality "

Steiner symmetrization is known not to increase perimeter of sets in Rn . The sets whose perimeter is preserved under this symmetrization are characterized in the present paper. 1. Introduction and main results 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.