相关论文: Extremal length in higher dimensions and complex s…

The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…

In this text, we explore the tools that Projective Differential Geometry can provide for the asymptotic analysis of classical fields on projectively compact manifolds. We emphasise on the case of order 2-compactifications and develop, in…

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…

We provide a numerical method to determine the critical lengths of linear differential operators with constant real coefficients. The need for such a procedure arises when the orders increase. The interest of this article is clearly on the…

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of…

We consider the problem of simultaneous approximation to a number and to its square in a general framework that encompasses imaginary quadratic number fields and fields of rational functions in one variable. In this context, we construct…

Volume is a natural measure of complexity of a Riemannian manifold. In this survey, we discuss the results and conjectures concerning n-dimensional hyperbolic manifolds and orbifolds of small volume.

We propose a novel ansatz, where the full black hole geometry is written as a linear in mass perturbation of the associated extremal black hole base. Contrary to its "standard" version, the corresponding "extremal Kerr-Schild form" is no…

The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…

It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of…

Extremal elements and a h-hull of sets in the n-dimensional hypercomplex space are investigated. Introduced a class of H-quasiconvex sets including strongly hypercomplex convex sets and being closed with respect to intersections.

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…

This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…

The interval numbers is the set of compact intervals of $\mathbb{R}$ with addition and multiplication operation, which are very useful for solving calculations where there are intervals of error or uncertainty, however, it lacks an…

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…

We discuss the Siciak-Zaharjuta extremal function of pluripotential theory for the unit ball in C^d for spaces of polynomials with the notion of degree determined by a convex body P. We then use it to analyze the approximation properties of…

Let $T$ be a triangulation of a Riemann surface. We show that the 1-skeleton of $T$ may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed…

We give a survey of classical and recent results on sharp constants and symmetry/asymmetry of extremal functions in $1$-dimensional functional inequalities.

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated…