Brunn-Minkowski Inequality

The th root of the content of the set sum of two sets in -dimensional Euclidean space is greater than or equal to the sum of the th roots of the contents of the individual sets.

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1/6 + 5/12 + 3/4
domain of f(x,y) = log(1-(x^2+y^2))
local extrema sin x^2

References

Cover, T. M. "The Entropy Power Inequality and the Brunn-Minkowski Inequality" §5.10 in Open Problems in Communications and Computation. (Ed. T. M. Cover and B. Gopinath). New York: Springer-Verlag, p. 172, 1987.Schneider, R. Convex Bodies: The Brunn-Minkowski Theory. Cambridge, England: Cambridge University Press, 1993.

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Brunn-Minkowski Inequality

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Weisstein, Eric W. "Brunn-Minkowski Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Brunn-MinkowskiInequality.html

Brunn-Minkowski Inequality

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References

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