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We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor…

A recent suggested definition of a relativistically correct three dimensional charge density of an extended hadron is shown to be physically and intuitively connected to an earlier relativistically correct two dimensional charge density…

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not.

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.

An analytical model for oscillating pair creation above the pulsar polar cap is presented in which the parallel electric field is treated as a large amplitude, superluminal, electrostatic wave. An exact formalism for such wave is derived in…

We prove that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a Kaehler surface.

We classify non-algebraic compact K\"ahler threefolds admitting an endomorphism $f: X \to X$ of degree at least two.

The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. That current includes, apart from the well-established delta-function term which is sufficient for its…

We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.

We put forward a fundamental relationship between the normalized spectral density of excess current noise and the imaginary part of complex conductivity.

In this paper we are dealing with quantitative Rellich inequalities on Finsler-Hadamard manifolds where the remainder terms are expressed by means of the flag curvature. By exploring various arguments from Finsler geometry and PDEs on…

We present examples, both compact and non-compact complete, of lo- cally non-homogeneous proper A-manifolds.

It is shown that CH implies the existence of a compact Hausdorff space that is countable dense homogeneous, crowded and does not contain topological copies of the Cantor set. This contrasts with a previous result by the author which says…

Using the chiral kinetic theory we derive the electric and chiral current densities in inhomogeneous relativistic plasma. We also derive equations for the electric and chiral charge chemical potentials that close the Maxwell equations in…

We continue the study of compact holomorphic $p$-contact manifolds $X$ that we introduced recently by expanding the discussion to include non-K\"ahler hyperbolicity issues and a differential calculus based on what we call the Lie derivative…

We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.

Stabilization and dispersion of electrical charge by colloids in non-polar media, such as nano-particles or inverse micelles, is significant for a variety of chemical and technological applications, ranging from drug delivery to e-ink. Many…

Let $X = M \times E$ where $M$ is an $m$-dimensional K\"ahler manifold with negative first Chern class and $E$ is an $n$-dimensional complex torus. We obtain $C^\infty$ convergence of the normalized K\"ahler-Ricci flow on $X$ to a…

Phase transitions, where observable properties of a many-body system change discontinuously, can occur in both open and closed systems. Ultracold atoms have provided an exemplary model system to demonstrate the physics of closed-system…

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…