Some Orlicz-Brunn-Minkowski type inequalities for (dual) quermassintegrals of polar bodies and star dual bodies have been introduced. In this paper, we generalize the results and establish some Orlicz-Brunn-Minkowski type inequalities for mixed (dual) quermassintegrals of polar bodies and star dual bodies.
In this paper, we establish a characterization of the polarity mapping for 1-dimensional convex bodies, which is a supplement to the result for such a characterization obtained by Böröczky and Schneider.
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