Perimeter under multiple Steiner symmetrizations

TL;DR

This paper investigates how applying multiple Steiner symmetrizations along linearly independent directions affects the perimeter of compact sets in R^n, showing that such transformations produce sets with finite perimeter.

Contribution

It provides new insights into the effects of multiple Steiner symmetrizations on the geometric properties of sets in Euclidean space.

Findings

Multiple Steiner symmetrizations result in sets of finite perimeter.

The perimeter of the transformed set can be controlled or estimated.

The process preserves certain geometric features of the original set.

Abstract

Steiner symmetrization along n linearly independent directions transforms every compact subset of R^n into a set of finite perimeter.