Minkowski Games

Minkowski Games

We introduce and study Minkowski games. In these games, two players take turns to choose positions in R based on some rules. Variants include boundedness games, where one player wants to keep the positions bounded (while the other wants to escape to infinity), and safety games, where one player wants to stay within a given set (while the other wants to leave it). We provide some general charact...

Minkowski Valuations

Centroid and difference bodies define SL(n) equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of SL(n) equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of SL(n) contravariant Minkowski valuations and of Lp-Minkowski valuations. 2000 AMS subject c...

The Brunn-Minkowski-Type Inequality

m-Projections involving Minkowski inverse and range symmetric property in Minkowski space

In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...

Existence of Minkowski space

Abstract Physics textbooks present Minkowski space as an almost pure mathematical construct, without any explicit restriction on a domain where it is applicable in physics. Meanwhile, its physical meaning cannot but follow the same premises as those which underlies the special relativity theory: motion of free point particles and propagation of electromagnetic waves. However, the common formali...