Related papers: The relative extremal function for Borel sets in c…

Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…

We study the existence of extremal functions on compact Riemannian manifold wich is locally Euclidean .

Extremal length is a classical tool in 1-dimensional complex analysis for building conformal invariants. We propose a higher-dimensional generalization for complex manifolds and provide some ideas on how to estimate and calculate it. We…

We give solutions to some extremal problems involving distance function in mixed norm spaces of harmonic functions on the unit ball of R^n

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

We compute the extremal plurisubharmonic function of the real torus viewed as a compact subset of its natural algebraic complexification.

The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.

We consider an extremal problem for polynomials, which is dual to the well-known Smale mean value problem. We give a rough estimate depending only on the degree.

We prove residual formulas for vector fields defined on compact complex orbifolds with isolated singularities and give some applications of these on weighted projective spaces.

On an odd-dimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel-Serre compactification of the manifold.…

We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…

We give geometrical conditions under which there exist extremal functions for the sharp $L^2$-Nash inequality.

We prove a formula for the Bergman kernel of polarized complex hyperbolic manifolds. The formula expresses the Bergman kernel as a sum over the geodesic loops in the manifold. As an application, we prove a result about the maximum and…

We construct a Borel maximal cofinitary group.

We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.

We give a sharp convexity estimate for L-functions which have a functional equation and an Euler product.

We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…

We generalize Lempert's and Poletsky's works on the description of extremal discs for the Kobayashi metric to a higher order setting.

We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…

We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and…