An inequality for Minkowski matrices

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...

Brunn - Minkowski Inequality

– We present a one-dimensional version of the functional form of the geometric Brunn-Minkowski inequality in free (noncommutative) probability theory. The proof relies on matrix approximation as used recently by P. Biane and F. Hiai, D. Petz and Y. Ueda to establish free analogues of the logarithmic Sobolev and transportation cost inequalities for strictly convex potentials, that are recovered ...

An inequality related to Minkowski type for Sugeno integrals

Article history: Received 2 April 2009 Received in revised form 16 March 2010 Accepted 22 March 2010

An Inequality for Permanents of (0,1)-Matrices*

Let A be an n-square (0, 1)-matrix, let ri denote the i-th row sum of A, i = 1 ..... n, and let per(A) denote the permanent of A. Then per(A) ~< H ri q~/-2,.1 I + V T where equality can occur if and only if there exist permutation matrices P and Q such that PAQ is a direct sum of l-square and 2-square matrices all of whose entries are 1. I f A = (ai~) is an n-square mat r ix then the permanent ...