Measuring the convexity of compact sumsets with the Schneider non-convexity index
Meyer, Mark
Meyer, Mark
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2025-01-01
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Article
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Sumset,Fractional partition,Lyusternik region,Convexity index
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Meyer, M. (2025). Measuring the convexity of compact sumsets with the Schneider non-convexity index. Journal of Inequalities and Applications. https://doi.org/10.1186/s13660-025-03356-w
Abstract
We study the Schneider non-convexity index of compact sets A?Rn, defined to be the smallest ?>0 such that the sumset A+?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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Springer Nature
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Journal of Inequalities and Applications
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1029242X
10255834
10255834