A Theorem on Convex Bodies of the Brunn-Minkowski Type

A Theorem on Convex Bodies of the Brunn-Minkowski Type.

* This work was supported by grants from Anheuser-Busch, Inc., American Cancer Society, and the U. S. Public Health Service. Leibowitz, J., and Hestrin, S., Advances in Enzymol., 5, 87-127 (1945). Lindegren, Carl C., Spiegelman, S., and Lindegren, Gertrude, PRoc. NAT. AcAD. Sci., 30, 346-352 (1944). Lindegren, Carl C., and Lindegren, Gertrude, Cold Spring Harbor Symposia Quant. Biol., 11, 115-1...

Some new Brunn-Minkowski-type inequalities in convex bodies

The Brunn-Minkowski inequality theory plays an important role in a number of mathematical disciplines such as measure theory, crystallography, optimal control theory, functional analysis, and geometric convexity. It has many useful applications in combinatorics, stochastic geometry, and mathematical economics. In recent years, several authors including Ball [1, 2, 3], Bourgain and Lindenstrauss...

The Brunn-Minkowski-Type Inequality

On the Equality Conditions of the Brunn-minkowski Theorem

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality. The Brunn-Minkowski Theorem asserts that, for compact convex sets K,L ⊆ Rn, the n-th root of the Euclidean volume Vn is concave with respect to Minkowski combinations; that is, for λ ∈ [0, 1], Vn((1− λ)K + λL) ≥ (1− λ)Vn(K) + λVn(L). The equality condition asserts that if K and L both have positive ...

the brunn-minkowski-type inequality