We provide a curvature flow approach to the regular Christoffel-Minkowski problem. The speed of our is an entropy preserving type and contains global term.

Abstract We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve regular Orlicz–Minkowski problems. As an application, we obtain old new results even problems; corresponding $$L_p$$ L p </mm...

For some self-similar sets K ⇢ R we obtain certain lower bounds for the lower Minkowski dimension of K + E in terms of the lower Minkowski dimension of E.

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem. Introduction Spacetime dia...

In Geometric Convexity, but also beyond its limits, isoperimetric inequalities have always played a central role. Applications of such inequalities can be found in Stochastic Geometry, Functional Analysis, Fourier Analysis, Mathematical Physics, Discrete Geometry, Integral Geometry, and various further mathematical disciplines. We will present a survey on isoperimetric inequalities in real, fin...

In this paper we have studied the nature of kinematical and dynamical laws in κ-Minkowski spacetime from a new perspective: the canonical phase space approach. We have introduced a new form of κ-Minkowski phase space algebra from which we recover the κ-extended finite Lorentz transformations derived in [13]. This is a particular form of a Deformed Special Relativity model that admits a modified...

This paper represents another step in overcoming a drawback of K-Means, its lack of defense against noisy features, by using feature weights in the criterion. The Weighted K-Means method by Huang et al. is extended to the corresponding Minkowski metric for measuring distances. Under Minkowski metric the feature weights become intuitively appealing feature rescaling factors in a conventional K-M...

The samples of geometric interpretation of space-time features of special relativity theory and phyllotaxis botanic phenomenon demonstrate variance of Minkovski’s theory application in mathematic modeling of natural phenomena. It is a well-known fact that in 1908, i.e. three years after A. Einstein’s theory of relativity was published, mathematician G. Minkowski made public geometric interpreta...