Minkowski's First Inequality For Convex Bodies - Statement of The Inequality

Statement of The Inequality

Let K and L be two n-dimensional convex bodies in n-dimensional Euclidean space Rn. Define a quantity V1(K, L) by

where V denotes the n-dimensional Lebesgue measure and + denotes the Minkowski sum. Then

with equality if and only if K and L are homothetic, i.e. are equal up to translation and dilation.

Read more about this topic:  Minkowski's First Inequality For Convex Bodies

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