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

Rigidity of Steiner's inequality for the anisotropic perimeter