Related papers: Some applications of metric currents to complex an…
We obtain a fine structural result for two-dimensional mod$(q)$ area-minimizing currents of codimension one, close to flat singularities. Precisely, we show that, locally around any such singularity, the current is a…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
We consider the category of all locally Lipschitz contractible metric spaces and all locally Lipschitz maps, which is a wide class of metric spaces, including all finite dimensional Alexandrov spaces and all CAT spaces. We also consider the…
We present a new algorithm for computing the electromagnetic fields of currents inside and outside of finite current sources, for arbitrary time variations in the currents. Unexpectedly, we find that our solutions for these fields are free…
We give a factorization of the fundamental cycle of an analytic space in terms of certain differential forms and residue currents associated with a locally free resolution of its structure sheaf. Our result can be seen as a generalization…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance.…
A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappinngs and Cartesian currents. Weak…
In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential…
Demailly showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents associated to subvarieties,…
We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence…
Understanding the behavior of quantum systems subject to magnetic fields is of fundamental importance and underpins quantum technologies. However, modeling these systems is a complex task, because of many-body interactions and because…
We extend the Cauchy residue theorem to a large class of domains including differential chains that represent, via canonical embedding into a space of currents, divergence free vector fields and non-Lipschitz curves. That is, while the…
Using an exact diagonalization technique within a generalized Mott-Hubbard Hamiltonian, we predict the existence of a ground state persistent current in coherent two-dimensional semiconductor quantum dot arrays pierced by an external…
In this paper, we analyze multi-dimensional Besicovitch almost periodic type functions. We clarify the main structural properties for the introduced classes of Besicovitch almost periodic type functions, explore the notion of…
Electricity plays a special role in our lives and life. Equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term the displacement current (of vacuum).…
Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversities has been developed which exhibits many deep analogies to…
We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…
We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the…
We study the space of Sasaki metrics on a compact manifold $M$ by introducing an odd-dimensional analogue of the $J$-flow. That leads to the notion of critical metric in the Sasakian context. In analogy to the K\"ahler case, on a polarised…