Calculus of Variations and Geometric Measure Theory

M. Perugini

Rigidity of Steiner's inequality for the anisotropic perimeter

created by perugini on 12 Nov 2019
modified on 29 Nov 2023


Published Paper

Inserted: 12 nov 2019
Last Updated: 29 nov 2023

Journal: Ann. Sc. norm. super. Pisa - Cl. sci
Year: 2022

ArXiv: 1911.03920 PDF


The aim of this work is to study the rigidity problem for Steiner's inequality for the anisotropic perimeter, that is, the situation in which the only extremals of the inequality are vertical translations of the Steiner symmetral that we are considering. Our main contribution consists in giving conditions under which rigidity in the anisotropic setting is equivalent to rigidity in the Euclidean setting. Such conditions are given in term of a restriction to the possible values of the normal vectors to the boundary of the Steiner symmetral (see Corollary 1.17, and Corollary 1.18).