We give the structure of discrete two-dimensional finite sets A, B ⊆ R2 which are extremal for the recently obtained inequality |A + B| ≥ ( |A| m + |B| n − 1)(m + n − 1), where m and n are the minimum number of parallel lines covering A and B respectively. Via compression techniques, the above bound also holds when m is the maximal number of points of A contained in one of the parallel lines co...

The Brunn–Minkowski Theorem asserts that μd(A+B)1/d ≥ μd(A) + μd(B) 1/d for convex bodies A,B ⊆ R , where μd denotes the d-dimensional Lebesgue measure. It is well known that equality holds if and only if A and B are homothetic, but few characterizations of equality in other related bounds are known. Let H be a hyperplane. Bonnesen later strengthened this bound by showing μd(A+B)≥ (M1/(d−1) +N1...

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the co...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

The main purposes of this paper are to establish some new Brunn– Minkowski inequalities for width-integrals of mixed projection bodies and affine surface area of mixed bodies, together with their inverse forms.

In this paper, we classify the nondegenerate ruled surfaces in three-dimensional Lorentz-Minkowski space that are translating solitons for inverse mean curvature flow. particular, prove existence of non-cylindrical solitons, which contrast with Euclidean setting.