Calculus of Variations and Geometric Measure Theory

F. Cagnetti - M. Colombo - G. De Philippis - F. Maggi

Rigidity of equality cases in Steiner's perimeter inequality

created by maggi on 06 Sep 2013
modified by dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 6 sep 2013
Last Updated: 30 oct 2017

Journal: Anal. PDE
Year: 2013

ArXiv: 1309.1639 PDF


Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to an hyperplane.

Keywords: Geometric measure theory, Symmetrization