The perimeter inequality under Steiner symmetrization: Cases of equality

Abstract

Steiner symmetrization is known not to increase perimeter of sets in $\mathbb{R}^n$. The sets whose perimeter is preserved under this symmetrization are characterized in the present paper.

Authors

Miroslav Chlebík

Max-Planck-Institut für Mathematik in den Naturwissenschaften, 04103 Leipzig, Germany

Andrea Cianchi

Dipartimento di Matematica, Università degli Studi di Firenze, 50134 Firenze, taly

Nicola Fusco

Facoltà di Scienze Matematiche Fisiche e Naturali, Università degli Studi di Napoli, 80126 Napoli, Italy