Related papers: Density currents and relative non-pluripolar produ…

A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…

We establish a relation between Lelong numbers and the full mass property of relative non-pluripolar products. We use it to show that if the restricted volume of a big cohomology class $\alpha$ in a compact K\"ahler $n$-dimensional manifold…

We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in K\"{a}hler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a…

In this paper, we study the geometry of pointwise semi-slant warped products in a locally conformal Kaehler manifold. In particular, we obtain several results which extend Chen's inequality for CR-warped product submanifolds in Kaehler…

In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.

We argue that an arbitrarily chosen time-dependent current density is generically non-Vrepresentable in a many-particle system, i.e., it cannot be obtained by applying only a time dependent scalar potential to the system. Furthermore we…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

In this work, we will verify some comparison results on Kahler manifolds. They are complex Hessian comparison for the distance function from a closed complex submanifold of a Kahler manifold with holomorphic bisectional curvature bounded…

In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact K\"ahler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact…

For a Kahler manifold X, we study a space of test functions W* which is a complex version of H1. We prove for W* the classical results of the theory of Dirichlet spaces: the functions in W* are defined up to a pluripolar set and the…

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…

We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak-strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.

Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued…

We produce new examples of non-K\"ahler complete expanding gradient Ricci solitons on trivial vector bundles over a product of Einstein manifolds with positive scalar curvature.

Astrophysical compact objects are studied in the context of quadratic non-metricity gravity. The solutions to the gravitational field equations, which include fluid components, are analyzed to investigate the density and pressure properties…

We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.

Let $X$ be a compact Kaehler manifold of dimension $k$ and $T$ be a positive closed current on $X$ of bidimension $(p,p)$ ($1\leq p < k-1$). We construct a continuous linear transform $\mathcal{L}_p(T)$ of $T$ which is a positive closed…

Currents in a few-electron parabolic quantum dot placed into a perpendicular magnetic field are considered. We show that traditional ways of investigating the Wigner crystallization by studying the charge density correlation function can be…

We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to…