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ASYMMETRIC Lp-DIFFERENCE BODIES

. Lutwak introduced the L p -diﬀerence body of a convex body as the Firey L p -combination of the body and its reﬂection at the origin. In this paper, we deﬁne the notion of asymmetric L p -diﬀerence bodies and study some of their properties. In particular, we determine the extremal values of the volumes of asymmetric L p -diﬀerence bodies and their polars, respectively.