Related papers: Decomposition of integral metric currents
We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in…
It is well known that in compact local Lipschitz neighborhood retracts in Euclidean space flat convergence for integer rectifiable currents amounts just to weak convergence. In the present paper we extend this result to integral currents in…
Every integral current in a locally compact metric space $X$ can be approximated by a Lipschitz chain with respect to the normal mass, provided that Lipschitz maps into $X$ can be extended slightly.
This paper proves an atomic decomposition of the space of $1$-dimensional metric currents without boundary, in which the atoms are specified by closed Lipschitz curves with uniform control on their Morrey norms. Our argument relies on a…
A comprehensive study of one-dimensional metric currents and their relationship to the geometry of metric spaces is presented. We resolve the one-dimensional flat chain conjecture in this general setting, by proving that its validity is…
We prove that every one-dimensional real Ambrosio-Kirchheim normal current in a Polish (i.e. complete separable metric) space can be naturally represented as an integral of simpler currents associated to Lipschitz curves. As a consequence a…
We consider an integrable model of a one-dimensional mesoscopic ring with the conduction electrons coupled by a spin exchange to a magnetic impurity. A symmetry analysis based on a Bethe Ansatz solution of the model reveals that the current…
The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective…
The integral expressions served to decompose vector field into irrotational and divergence-free components represent modern version of the Helmholtz decomposition theorem. These expressions are also widely used to decompose the…
Motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations, this work develops a theory of space-time integral currents with bounded variation in time, which enables a natural variational approach…
We show that the members of the Lipschitz-free space of $[-1,1]^n$ are exactly the 0-dimensional flat currents whose "boundary" vanishes. The connection with normal and flat currents allows to use the Federer-Fleming compactness and…
We present some results concerning currents of integration on finite-dimensional analytic spaces in Hilbert spaces, using the setting of metric currents. In particular, we obtain the characterization of such currents as positive closed…
It is well known that each nonnegative integral flow on a graph can be decomposed into a sum of nonnegative graphic circuit flows, which cannot be further decomposed into nonnegative integral sub-flows. This is equivalent to saying that the…
We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be…
We prove several results on Almgren's multiple valued functions and their links to integral currents. In particular, we give a simple proof of the fact that a Lipschitz multiple valued map naturally defines an integer rectifiable current;…
One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration…
We compare singular homology and homology via integral currents in metric spaces that are homeomorphic to smooth manifolds. For such spaces, we provide sufficient conditions that guarantee the existence of a surjective homomorphism from the…
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…
A divergence-free horizontal vector current in Heisenberg space may be viewed as an element of the dual space of horizontal test vector fields. By applying a horizontal Liouville theorem in this setting, the flow lines of such a vector…