Measuring the convexity of compact sumsets with the Schneider non-convexity index

Key Points

• The study calculates a sharp lower bound on the schneider non-convexity index for the minkowski sum of compact sets.
• A family of fractional subadditive inequalities for sums of multiple compact sets is established, enhancing understanding of their properties.
• The research focuses on the convexity characteristics of sumsets formed from compact sets in Rn, highlighting their mathematical significance.
• The findings may have implications for mathematical analysis and optimization involving compact sets.