Related papers: Some applications of metric currents to complex an…
The emphasis of this course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic functions and on the theory of positive closed currents. Applications of…
We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension.
The standard arithmetic measures of center, the mean and median, have natural topological counterparts which have been widely used in continuum theory. In the context of metric spaces it is natural to consider the Lipschitz continuous…
In this paper we present a new approach to Morse theory based on the de Rham-Federer theory of currents. The full classical theory is derived in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic…
In many problems of PDE involving the Laplace-Beltrami operator on manifolds with ends, it is often useful to introduce radial or geodesic normal coordinates near infinity. In this paper, we prove the existence of such coordinates for a…
A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved $U(1)$ currents $J^a$. We propose a quantum formulation of these deformations, based on the gauging…
In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…
This paper aims to define and study currents and slices of currents in the Heisenberg group $\mathbb{H}^n$. Currents, depending on their integration properties and on those of their boundaries, can be classified into subspaces and, assuming…
A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric…
We introduce a notion of super-potential (canonical function) associated to positive closed (p,p)-currents on compact Kaehler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of…
Calculation of current and order parameter distribution in inhomogeneous superconductors is often based on a self-consistent solution of Eilenberger equations for quasiclassical Green's functions. Compared to the original Gorkov equations,…
We propose a new strong Riemannian metric on the manifold of (parametrized) embedded curves of regularity $H^s$, $s\in(3/2,2)$. We highlight its close relationship to the (generalized) tangent-point energies and employ it to show that this…
We define a formal Riemannian metric on a given conformal class of metrics on a closed Riemann surface. We show interesting formal properties for this metric, in particular the curvature is nonpositive and the Liouville energy is…
We define the pull-back operator, associated to a meromorphic transform, on several types of currents. We also give a simple proof to a version of a classical theorem on the extension of currents.
We offer an example of the second order Kawaguchi metric function the extremal flow of which generalizes the flat space-time model of the semi-classical spinning particle to the framework of the pseudo-Riemannian space-time. The general…
This paper provides a functional analytic approach to differential equations on Banach space with slowly evolving parameters. We develop a Fenichel-like theory for attracting subsets of critical manifolds via a Lyapunov-Perron method. This…
Time measurements are routinely preformed in laboratories, nevertheless their theoretical account presents some difficulties and for actual experiments an approximate, semiclassical expression is always used. Here, we will discuss their…
Surface sensitive electric current measurements are important experimental tools poorly corroborated by theoretical models. We show that the drift-diffusion equations offer a framework for a consistent description of such experiments. The…