相关论文: Growth of balls of holomorphic sections and energy…

We consider a thin multidomain of $\mathbb R^3,$ consisting of a vertical rod upon a horizontal disk. The equilibrium configurations of the thin hyperelastic multidomain, allowing for fracture and damage, are described by means of a bulk…

The energy-momentum distribution of spatially homogeneous rotating spacetimes in the context of teleparallel theory of gravity is investigated. For this purpose, we use the teleparallel version of Moller prescription. It is found that the…

Let $X=\mathbb{C}\times\Sigma$ be the product of the complex plane and a compact Riemann surface. We establish a classification theorem of solutions to the Seiberg-Witten equation on $X$ with finite analytic energy. The spin bundle $S^+\to…

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we…

We consider a gauge-invariant Ginzburg-Landau functional (also known as Abelian Yang-Mills-Higgs model) on Hermitian line bundles over closed Riemannian manifolds of dimension $n \geq 3$. Assuming a logarithmic energy bound in the coupling…

Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…

We introduce the notion of tubular dimension, and give a formula for it. As an application we show that every invariant measure of a $C^{1+\gamma}$ diffeomorphism of a closed Riemannian manifold admits an asymptotic local product structure…

We study mathematically the equilibrium properties of the Bose-Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the…

We consider two related problems: the first is the minimization of the "Coulomb renormalized energy" of Sandier-Serfaty, which corresponds to the total Coulomb interaction of point charges in a uniform neutralizing background (or rather…

Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric…

We extend the `topological inflation' of Linde and Vilenkin to {\em unstable} monopoles. This allows the monopole to decay; not inflating eternally, as topological inflation demands. Such a situation happens naturally in some Grand Unified…

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to…

We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a particular external field. We show that this problem admits a…

Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a…

On extending the Standard Model (SM) Lagrangian, through a non-linear Born-Infeld (BI) hypercharge term with a parameter $\beta$ (of dimensions of [mass]$^2$), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze [1].…

We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the…

This note is an addendum to the paper `Global pluripotential theory over a trivially valued field' by the present authors, in which we prove two results. Let $X$ be an irreducible projective variety over an algebraically closed field field…

We show that in the dual version of the generalized Dick model monopole-anti-monopole pairs have finite energy. It is possible to use the potential between monopole and anti-monopole to find the mass spectrum of the glueballs. The results…

In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…

Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the heat equation. Additionally, for the homogeneous equation, we…