On the equality conditions of the Brunn-Minkowski theorem

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 effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...

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...

The Brunn-Minkowski-Type Inequality

The Brunn-Minkowski Inequality

In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of Rn, and deserves to be better known. This guide explains the relationship between the Brunn-Minkowski inequality and other inequalities in geometry and analysis, an...