Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and ...

abstract issue: in economic literature, there are two hypotheses regarding the link between economic development and gender inequality. the first gender inequality decreases with economic development. second, economic development increases gender inequality. this research is conducted to investigate the effects of economic development on gender inequality according to kuznets gender curve in ir...

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose–type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow with work done by Shi–Tam regarding boundary behavior of compact manifolds. As...

1.1. Statement of the main result. The isoperimetric problem of euclidean type for a space X and given classes Ik−1, Ik, and Ik+1 of surfaces of dimension k − 1, k, and k + 1 in X , together with boundary operators Ik+1 ∂ −→ Ik ∂ −→ Ik−1 and a volume function M on each class, asks the following: Does there exist for every surface T ∈ Ik without boundary, ∂T = 0, a surface S ∈ Ik+1 with ∂S = T a...

The Brunn-Minkowski inequality theory plays an important role in a number of mathematical disciplines such as measure theory, crystallography, optimal control theory, functional analysis, and geometric convexity. It has many useful applications in combinatorics, stochastic geometry, and mathematical economics. In recent years, several authors including Ball [1, 2, 3], Bourgain and Lindenstrauss...