The study computes a lower bound on the schneider non-convexity index for compact sets, suggesting new inequalities.
We study the Schneider non-convexity index of compact sets A⊂ Rⁿ , defined to be the smallest λ >0 such that the sumset A+λ conv(A) is convex. We compute a sharp lower bound on the index of the Minkowski sum of two compact sets in R , and establish a family of fractional subadditive inequalities for sums of m compact sets in Rⁿ .
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Mark Meyer (2025) studied this question.
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