Related papers: Density currents and relative non-pluripolar produ…
Harvey and Lawson introduced the Kaehler rank and computed it in connection to the cone of positive exact currents of bidimension (1,1) for many classes of compact complex surfaces. In this paper we extend these computations to the only…
Let $K_\varphi$ denote the weighted Bergman kernel associated to a plurisubharmonic function $\varphi$. We obtain upper bounds and positive lower bounds for the Bergman metric $i\partial \bar{\partial} \log K_\varphi$, expressed solely in…
Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X,\phi). In particular, on X there exist \phi-plurisubharmonic functions, \phi-convex domains, \phi-convex boundaries, etc., all…
The time derivative of the charge density is linked to the current density by the continuity equation. However, it features only the longitudinal part of a current density, which is known to produce no radiation. This fact usually remains…
We propose that under certain conditions heterotic string compactifications on half-flat and nearly-Kahler manifolds are equivalent. Based on this correspondence we argue that the moduli space of the nearly-Kahler manifolds under discussion…
Dipolar bilayers with antiparallel polarization, i.e. opposite polarization in the two layers, exhibit liquid-like rather than gas-like behavior. In particular, even without external pressure a self-bound liquid puddle of constant density…
A recent theorem of Diverio--Trapani and Wu--Yau asserts that a compact K\"ahler manifold with a K\"ahler metric of quasi-negative holomorphic sectional curvature is projective and canonically polarized. This confirms a long-standing…
In the present paper, we show that given a compact K\"ahler manifold $(X,\omega)$ with a K\"ahler metric $\omega$, and a complex submanifold $V\subset X$ of positive dimension, if $V$ has a holomorphic retraction structure in $X$, then any…
Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables (the current density and the superconducting order parameter, respectively) are included in the…
We study non-commutative degenerations of elliptic curves over local fields. The corresponding objects are close relatives of non-commutative tori of Connes and Rieffel.
The static current operator leads to definitional zero frequency divergence and unphysical results in studying nonlinear optical susceptibilities of polymers. A well-defined dipole-dipole correlation is superior to the complicated…
We consider a nondegenerate holomorphic map $f: V \mapsto X$ where $(X, \omega)$ is a compact hermitian manifold of dimension higher or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$. In this article we give…
Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noise combined with Poisson point processes, and product systems are much more diverse than Fock spaces. This text is a…
We discuss the current conservation laws in sigma models based on a compact Lie groups of the same dimensionality and connected to each other via pseudoduality transformations in two dimensions. We show that pseudoduality transformations…
The transient electric current of surfactants dissolved in a nonpolar solvent is investigated both experimentally and theoretically in the parallel-plate geometry. Due to a low concentration of free charges the cell can be completely…
We show that in every dimension greater than or equal to 4, there exist compact Kaehler manifolds which do not have the homotopy type of projective complex manifolds. Thus they a fortiori are not deformation equivalent to a projective…
We provide a counterexample to a conjecture by B. Connelly about density of circle packings
The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.
Longitudinal non-dissipative current states in bilayer electron-hole systems in the presence of potential barriers that divide the system into left and right sides was investigated. The consideration is performed both for the case of weak…
In this paper, we prove conjugate radius estimate, volume comparison and rigidity theorems for K\"ahler manifolds with various curvature conditions.