Related papers: Super-potentials of positive closed currents, inte…

Pseudopotential theory has greatly driven first-principles calculations in materials, replacing the explicit treatment of the chemically inert core electrons with an effective potential acting only on the valence states. This is inherently…

For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of…

In this study we extend the concepts of $m$-pluripotential theory to the Riemannian superspace formalism. Since in this setting positive supercurrents and tropical varieties are closely related, we try to understand the relative capacity…

We construct integrable pseudopotentials with an arbitrary number of fields in terms of elliptic generalization of hypergeometric functions in several variables. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic…

Let $X$ be a compact K\"ahler manifold of dimension 3 and let $f:X\rightarrow X$ be a pseudo-automorphism. Under the mild condition that $\lambda_1(f)^2>\lambda_2(f)$, we prove the existence of invariant positive closed $(1,1)$ and $(2,2)$…

We construct $d$-closed and $dd^c$-closed positive currents associated to a holomorphic map $\phi$ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area…

We construct the Green current for a random iteration of "horizontal-like" mappings in two complex dimensions. This is applied to the study of a polynomial map $f:\mathbb{C}^2\to\mathbb{C}^2$ with the following properties: 1. infinity is…

In this article, we consider currents given by the p-fold non-pluripolar product associated with a quasi-plurisubharmonic function of finite energy, and prove that normalized pull-backs of such currents converge to the Green (p, p)-current…

Let $f$ be a polynomial automorphism of ${\Bbb C}^k$ of degree $\lambda$, whose rational extension to ${\Bbb P}^k$ maps the hyperplane at infinity to a single point. Given any positive closed current $S$ on ${\Bbb P}^k$ of bidegree (1,1),…

Let $T$ be a positive closed current of unit mass on the complex projective space $\mathbb P^n$. For certain values $\alpha<1$, we prove geometric properties of the set of points in $\mathbb P^n$ where the Lelong number of $T$ exceeds…

Two dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on `capacitor-like' geometries with current flowing between two…

A wide and natural class of closed currents - which are differences of positive closed currents - can be constructed by pulling back smooth closed forms using rational maps. These currents are very singular in general, and hence defining…

Let f be a holomorphic automorphism of a compact Kahler manifold (X,\omega) of dimension k>1. We study the convex cones of positive closed (p,p)-currents T_p, which satisfy a functional relation $f^*(T_p)=\lambda T_p, \lambda>1,$ and some…

In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…

Interest in Josephson junctions (JJs) has increased rapidly in recent years not only because of their use in qubits and other quantum devices but also due to the unique physics supported by the JJs. The advent of various novel quantum…

In this paper we review the use of techniques of positive currents for the study of parameter spaces of one-dimensional holomorphic dynamical systems (rational mappings on P^1 or subgroups of the Moebius group PSL(2,C)). The topics covered…

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…

Superconductors used in magnet technology could carry extreme currents because of their ability to keep the magnetic flux motionless. The dynamics of the magnetic flux interaction with superconductors is controlled by this property. The…

The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical…

Let $T$ be a positive closed current of bidegree $(1,1)$ on a multiprojective space $X={\mathbb P}^{n_1}\times\ldots\times{\mathbb P}^{n_k}$. For certain values of $\alpha$, which depend on the cohomology class of $T$, we show that the set…