An r -hyperconvex body is a set in the d -dimensional Euclidean space đź d that is the intersection of a family of closed balls of radius r . We prove the analogue of the classical BlaschkeâSantalĂł inequality for r -hyperconvex bodies, and we also establish a stability version of it. The other main result of the paper is an r -hyperconvex version of the reverse isoperimetric inequality in the plane.
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Fodor et al. (2016) studied this question.
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