The equality cases in Steiner's projection inequality

摘要

In Lin (Calc. Var. Partial Differential Equations 60:196, 2021), the first author proved the Steiner's projection inequality and the Petty projection inequality for sets of finite perimeter but didn't characterize their cases of equality. In this paper, we characterize the case of equality in the Steiner's projection inequality. Moreover, we give a new proof of the equality case in the Petty projection inequality, which was characterized by Wang (Adv. Math. 230:2457-2473, 2012).

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