Related papers: On the tangent cones to plurisubharmonic currents
This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…
We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly…
In this paper we show that, if $T$ is an area-minimizing $2$-dimensional integral current with $\partial T = Q [\![ \Gamma ]\!]$, where $\Gamma$ is a $C^{1,\alpha}$ curve for $\alpha>0$ and $Q$ an arbitrary integer, then $T$ has a unique…
We prove several results showing that plurisubharmonic functions with various bounds on their Monge-Ampere masses on a bounded hyperconvex domain always admit global plurisubharmonic subextension with logarithmic growth at infinity.
In equilibrium, the number of conduction electrons in a solid substance depends on the conformation of the atoms in the substance. When a magnetic field is applied, it takes time for the system to come to a new equilibrium with a new…
In multichannel rings, evanescent modes will always co-exist with propagating modes. The evanescent modes can carry a very large diamagnetic persistent current that can oscillate with energy and are very sensitive to impurity scattering.…
Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford--Taylor product for Lagerberg currents on open…
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of length functions to counting problems. Secondly, we use…
The spin resolved current shot noise can uniquely probe the interactions in mesoscopic systems: i) in a normal-superconducting junction, the spin current noise is zero, as carried by singlets, and ii) in a single electron transistor (SET)…
In this article we establish several Ohsawa-Takegoshi type theorems for twisted pluricanonical forms and metrics of adjoint $\bR$-bundles.
We will consider here some dynamics of the tangent map, weaker than hyperbolicity, and we will discuss if these structures are rich enough to provide a good description of the dynamics from a topological and geometrical point of view. This…
Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the…
Persistent current and low-field magnetic susceptibility in single-channel normal metal rings threaded by a magnetic flux $\phi$ are investigated within the tight-binding framework considering long-range hopping of electrons in the {\em…
We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex…
We propose an approach allowing the computation of currents and their correlations in interacting multiterminal mesoscopic systems involving quantum dots coupled to normal and/or superconducting leads. The formalism relies on the expression…
The basic stages of development of the theory of superconductivity are traced. Despite of remarkable successes of theory, the physical explanation of the phenomenon of superconductivity - of the not fading electrical current in dissipative…
In this paper, we study the relationship between the dimension of linear space of harmonic function with growth bounded by a fixed-degree polynomial on a minimal submanifold in Euclidean space and that on its one cylindrical tangent cone at…
We will define the Monge-Amp\`ere operator on finite (weakly) plurifinely plurisubharmonic functions in plurifinely open sets in complex n-space and show that it defines a positive measure. Ingredients of the proof include a direct proof…
In this short note, we would like to give a construction of parallel transport for tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete proof for the linear part of the tangent space, and show that a…