Fuchsian convex bodies: basics of Brunn--Minkowski theory

123.. within critical media theory generally, between: 1) a tendency to engage more intimately with the physical technology of the media, on its own terms, to engage with

This inequality is proved by using a generalization of the Petty projection inequality to compact sets that is established in this paper (see 30], 31], 16], 26], 38] and 42] for

The main result of the present theoretical paper is an original decomposition formula for the proximal operator of the sum of two proper, lower semicontinuous and convex functions f

The objects of each theories are fellows: to the compact sets in the Brunn-Minkowski theory correspond the random vectors in the Information theory, the Gaussian random vectors play

A technical element of this proof that we believe of independent interest is the Poincaré-type trace inequality on convex sets proved in Section 2, with a constant having

In the second part of the paper, we show that every metric measure space satisfying the classical Brunn-Minkowski inequality can be approximated by discrete metric spaces with

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DCMMR(PI> ^I) by a linear time algorithm. The algorithm discussed in Section 3 below for the case of disjoint polygons is an adaptation of that presented in Atallah [1983] and