Abstract
We improve the Brunn–Minkowski inequality for nonconvex sets. Besides the volume of the sets, our estimate depends on the volume of the convex hull of one of the sets. The estimate is asymptotically the best possible if this set is fixed and the size of the other tends to infinity.
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Ruzsa, I.Z. The Brunn–Minkowski Inequality and Nonconvex Sets. Geometriae Dedicata 67, 337–348 (1997). https://doi.org/10.1023/A:1004958110076
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DOI: https://doi.org/10.1023/A:1004958110076