When does Brunn-Minkowski inequatily $(m(A+B))^{1/d} \geqslant (m(A))^{1/d} + (m(B))^{1/d}$ become equality?

You might also be interested in the following two papers by Fields medalist A. Figalli:

  • Quantitative stability for the Brunn-Minkowski inequality,
  • Stability result for the Brunn-Minkowski inequality.

The stability result, proven with optimal transport techniques, implies in particular the equality condition.

Tags:

Real Analysis

Measure Theory

Geometric Measure Theory

Lebesgue Measure

Convex Analysis

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