Sharp pointwise gradient estimates for Riesz potentials with a bounded density

We establish sharp inequalities for the Riesz potential and its gradient in $\mathbb{R}^{n}$ and indicate their usefulness for potential analysis, moment theory and other applications.Comment: 14 pages, submitted to Analysis and Mathematical Physic

V.M. Miklyukov: from dimension 8 to nonassociative algebras

In this short survey we give a background and explain some recent developments in algebraic minimal cones and nonassociative algebras. A good deal of this paper is recollections of my collaboration with my teacher, PhD supervisor and a colleague, Vladimir Miklyukov on minimal surface theory that motivated the present research. This paper is dedicated to his memory.Comment: 19 page