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...

We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a Brunn-Minkowski inequality and an Urysohn’s type inequality for the Bernoulli Constant and we study the behaviour of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior non-linear Bernoulli problem.

It is well-known that the Hölder-Rogers inequality implies the Minkowski inequality. Infantozzi [6] observed implicitely and Royden [15] proved explicitely that the reverse implication is also true. In this note we discuss and give a new proof of this perhaps surprising fact. Mathematics subject classification (2000): 26D15.

In this paper we establish the Lp-Minkowski inequality and Lp-Aleksandrov-Fenchel type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies, respectively. As applications, we get some related results. The paper new contributions that illustrate this duality of projection and intersection bodies will be presented. M.S.C. 2000: 52A40.

We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman’s reverse Brunn-M...

In this paper, connections are uncovered between the averaged weak (AWEC) and averaged null (ANEC) energy conditions, and quantum inequality restrictions (uncertainty principle-type inequalities) on negative energy. In twoand four-dimensional Minkowski spacetime, we examine quantized, free massless, minimally-coupled scalar fields . In a two-dimensional spatially compactified Minkowski universe...

We prove an inequality of the form γn ≥ Cn(γn−1) between Hermite’s constants γn and γn−1. This inequality yields also a new proof of the Minkowski-Hlawka bound ∆n ≥ ζ(n)21−n for the maximal density ∆n of n−dimensional lattice-packings. 1

We prove the existence and uniqueness up to translations of the solution to a Minkowski type problem for the torsional rigidity in the class of open bounded convex subsets of R n. For the existence part we apply the variational method introduced by Jerison in: Adv. Math. 122 (1996), pp. 262–279. Uniqueness follows from the Brunn–Minkowski inequality for the torsional rigidity and corresponding ...