We define complex super Minkowski space time in 4 dimensions as the big cell inside a complex super flag manifold. The complex superconformal group acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex super Minkowski space time. We then consider real super Minkowski space time as a suitable real form of the complex version. Our methods are ...

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed and proved to be true in some significant special cases. Th...

For the closed relativistic string carrying a pointlike mass the exact solutions of the dynamical equations are obtained and studied. These solutions describe states of the mentioned system moving in Minkowski space and also in the space that is the direct product of Minkowski space and a compact manifold (torus). We consider the closed relativistic string with one massive point (homeomorphic t...

We argue that “effective” superluminal travel, potentially caused by the tipping over of light cones in Einstein gravity, is always associated with violations of the null energy condition (NEC). This is most easily seen by working perturbatively around Minkowski spacetime, where we use linearized Einstein gravity to show that the NEC forces the light cones to contract (narrow). Given the NEC, t...

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we giv...

We show that all harmonic morphisms from 3-dimensional Minkowski space with values in a surface have a Weierstrass representation involving the complex numbers or the hyperbolic numbers depending on the signature of the codomain. We deduce that there is a nontrivial globally defined submersive harmonic morphism from Minkowski 3-space to a surface, in contrast to the Riemannian case. We show tha...

In 1905 Hermann Minkowski introduced his theory of reduction of positive definite quadratic forms. Recently, Hans J. Zassenhaus has suggested that this theory can be applied to the problem of row reduction of matrices of integers. Computational investigations have shown that for matrices with more columns than rows, the number of steps required for reduction decreases drastically. In this paper...

Rotation intertwining maps from the set of convex bodies in R into itself that are continuous linear operators with respect to Minkowski and Blaschke addition are investigated. The main focus is on Blaschke-Minkowski homomorphisms. We show that such maps are represented by a spherical convolution operator. An application of this representation is a complete classification of all even BlaschkeMi...

The Abraham-Minkowski dilemma relates to the disputed value of the optical momentum within a dielectric medium and whether the free-space value should be divided (Abraham) or multiplied (Minkowski) by the refractive index. Although undoubtedly simplistic, these two approaches provide intuitive insight to many subtle problems in optical physics. This paper reviews a modified version of the Einst...

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and shown to be best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed, and proved to be true in some significant special cases. Througho...