Related papers: Extremal functions on moduli spaces and applicatio…

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $A^p_\alpha$ where $-1 < \alpha < 0$ and $-1 < \alpha < p-2$. We obtain bounds on how close the approximation is to the true extremal function in…

General results on convex bodies are reviewed and used to derive an exact closed-form parametric formula for the Minkowski sum boundary of $m$ arbitrary ellipsoids in $N$-dimensional Euclidean space. Expressions for the principal curvatures…

We present an explicit method to compute the (Siciak-Zaharjuta) extremal function of a real convex polytope in terms of supporting simplices and strips. We use this to give a new proof of the existence of extremal ellipses associated to the…

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 analyse the relationship between different extremal notions in Lipschitz free spaces (strongly exposed, exposed, preserved extreme and extreme points). We prove in particular that every preserved extreme point of the unit ball is also a…

Classical extremal length (or conformal modulus) is a conformal invariant involving families of paths on the Riemann sphere. In ``Extremal length and functional completion'', Fuglede initiated an abstract theory of extremal length which has…

We investigate deformations of extremal near-horizon geometries in Einstein-Maxwell-Dilaton theory, including various topological terms, and also in D=11 supergravity. By linearizing the field equations and Bianchi identities over the…

We focus on two dependency quantities of a max-stable random field $X$ on some space $T$: the extremal coefficient function $\theta$ which we define on finite sets of $T$ and the extremal correlation function $\chi(s,t)=\lim_{x \uparrow…

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,…

In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is shown that the intersection of a suitable ball with the…

Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $\mathfrak x$, we try to maximize the…

With any convex function F on a finite-dimensional linear space X such that F goes to infinity at infinity, we associate a Borel measure on the dual space X*. This measure is obtained by pushing forward the measure exp(-F(x))dx under the…

For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of…

We present a unified description of extremal metrics for the Laplace and Steklov eigenvalues on manifolds of arbitrary dimension using the notion of $n$-harmonic maps. Our approach extends the well-known results linking extremal metrics for…

We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space $M$ is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to formulate a general…

Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.

In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplectic toric geometry. By using these observations, we derive…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…

We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a…