Related papers: On different extremal bases for $\CC$-convex domai…

We study balls of homogeneous cubics on $\mathbb R^n$, $n = 2,3$, which are bounded by unity on the unit sphere. For $n = 2$ we completely describe the facial structure of this norm ball, while for $n = 3$ we classify all extremal points…

A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…

The purpose of this study is to investigate two related spatial branching models with the unbounded branching intensity. The objective is to describe the asymptotic behaviour of the extremal particle.

In this paper, we explore the geometric properties of unbounded extremal domains for the $p$-Laplacian operator in both Euclidean and hyperbolic spaces. Assuming that the nonlinearity grows at least as the nonlinearity of the eigenvalue…

Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…

This article is based on papers discussing different aspects of extra dimensional environments. In addition to the results, we review some of the concepts on which models with large extra dimensions are based.

The main result of this paper is that for any norm on a complex or real $n$-dimensional linear space, every extremal basis satisfies inverted triangle inequality with scaling factor $2^n-1$. Furthermore, the constant $2^n-1$ is tight. We…

In this paper one finds:1) A simple combinatorical description of the distinguished boundary of the crown domain in terms of the affine Weyl group; 2) Optimal upper and lower bounds for holomorphically extended spherical functions; 3) First…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as…

We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

This article investigates various notions of primeness for one-sided ideals in noncommutative rings, with a focus on principal ideal domains.

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.

In this short note we consider very general bounded minimal homogeneous domains. Under certain natural additional conditions new sharp results on Bergman type analytic spaces in minimal bounded homogeneous domains are obtained. Domains we…

In this paper, we show that the convex domains of the hyperbolic space which are almost extremal for the Faber-Krahn or the Payne-Polya-Weinberger inequalities are close to geodesic balls. Our proof is also valid in other space forms and…

We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for…

We establish a spatial gradient maximum principle for classical solutions to the initial and Neumann boundary value problem of some quasilinear parabolic equations on smooth convex domains.

We obtain sharp lower bounds on the radii of inscribed balls for strictly convex isoperimetric domains lying in a 2-dimensional Alexandrov metric space of curvature bounded below. We also characterize the case when such bounds are attained.

The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…