相关论文: On the Capacity of Eilenberg-MacLane and Moore Spa…

K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the concept of the capacity of a compactum and raised some interesting questions about it. In this paper, during computing the capacity of wedge sum of finitely many…

K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the concept of the capacity of a compactum. In this paper, we compute the capacity of the product of two spheres of the same or different dimensions and the capacity of…

K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the concept of capacity and depth of a compactum. In this paper, we compute the capacity and depth of compact surfaces. We show that the capacity and depth of every…

K. Borsuk in the seventies introduced the notions of capacity and depth of compacta together with some relevant problems. In this paper, first, we introduce the concepts of the (strong) capacity and the (strong) depth of an object in an…

The purpose of this article is to define a capacity on certain topological measure spaces $X$ with respect to certain function spaces $V$ consisting of measurable functions. In this general theory we will not fix the space $V$ but we…

For compact subsets $E$ of the unit disk $ \mathbb{D}$ we study the capacity of the condenser ${\rm cap}( \mathbb{D},E)$ by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of…

The modulus metric (also called the capacity metric) on a domain $D\subset \mathbb{R}^n$ can be defined as $\mu_D(x,y)=\inf\{{\mbox{cap}}\,(D,\gamma)\}$, where ${\mbox{cap}}\,(D,\gamma)$ stands for the capacity of the condenser $(D,\gamma)$…

The aim of this note is to study the convergence in capacity for functions in the class $\mathcal E(X,\omega)$. We obtain several stability theorems. Some of these are (optimal) generalizations of results of Xing, while others are new.

We obtain in this paper bounds for the capacity of a compact set $K$. If $K$ is contained in an $(n+1)$-dimensional Cartan-Hadamard manifold, has smooth boundary, and the principal curvatures of $\partial K$ are larger than or equal to…

We study the conformal capacity ${\rm cap}(\Omega,K)$ where $\Omega$ is a bounded domain of $\mathbb{R}^2$ and $K$ is a compact connected set in $\Omega$. Because the exact numerical value of the capacity is known only in a handful of…

The paper deals with the theory of inner (outer) capacities on locally compact spaces with respect to general function kernels, the main emphasis being placed on the establishment of alternative characterizations of inner (outer) capacities…

We generalise some results of R. E. Stong concerning finite spaces to wider subclasses of Alexandroff spaces. These include theorems on function spaces, cores and homotopy type. In particular, we characterize pairs of spaces X,Y such that…

We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M. When M is non-compact, R is homotopically equivalent to M,…

The class of $L\Sigma(\leq\omega)$-spaces was introduced in 2006 by Kubi\'s, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindel\"of $\Sigma$-spaces. Compact $L\Sigma(\leq\omega)$-spaces were…

For $p \in (1,N)$ and $\Omega \subseteq \mathbb{R}^N$ open, the Beppo-Levi space $\mathcal{D}^{1,p}_0(\Omega)$ is the completion of $C_c^{\infty}(\Omega)$ with respect to the norm $\left( \int_{\Omega}|\nabla u|^p \right)^ \frac{1}{p}.$…

In this article we study two classical potential-theoretic problems in convex geometry corresponding to a nonlinear capacity, $\mbox{Cap}_{\mathcal{A}}$, where $\mathcal{A}$-capacity is associated with a nonlinear elliptic PDE whose…

We find an asymptotic formula for the conformal capacity of a plane condenser both plate of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear…

Let $(M,g)$ be a $3$--dimensional, complete, one--ended Riemannian manifold, with a minimal, compact and connected boundary. We assume that $M$ has a simple topology and that the scalar curvature of $(M,g)$ is non--negative. Moreover, we…

Here, the concept of electric capacity on Finsler spaces is introduced and the fundamental conformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact Finsler manifold is conformal invariant. This…

The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multiple natural definitions of capacity are possible). Motivated…