Related papers: Weighted Green functions for complex Hessian opera…

The Lempert function for several poles $a_0, ..., a_N$ in a domain $\Omega$ of $\mathbb C^n$ is defined at the point $z \in \Omega$ as the infimum of $\sum^N_{j=0} \log|\zeta_j|$ over all the choices of points $\zeta_j$ in the unit disk so…

In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifold. In the same context and for…

We conjecture that quantum Gaudin models in affine types admit families of local higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are given by functions on a space of meromorphic opers associated…

We compute the Green's function for the Hodge Laplacian on the symmetric spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and \Sigma is a simply connected Riemannian…

For $p_1,...,p_n>0$, let $\mathbb E=\{z\in\mathbb C^n:\sum_{j=1}^n|z_j|^{2p_j}<1\}$ be a complex ellipsoid. We present effective formulas for the generalized M\"obius and Green functions $m_{\mathbb E}(A,\cdot)$, $g_{\mathbb E}(A,\cdot)$ in…

The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the…

We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and…

We study the dynamics of polynomial skew products on C^2. By using suitable weights, we prove the existence of several types of Green functions. Largely, continuity and plurisubharmonicity follow. Moreover, it relates to the dynamics of the…

Here we obtain bounds on the spectrum of that operator whose inverse, when it exists, gives the Green's function. We consider the wide of physical problems that can be cast in a form where a constitutive equation ${\bf J}({\bf x})={\bf…

In this paper it is shown that if $\Omega \subset \mathbb{R}^N$ is an open, bounded Lipschitz set, and if $f: \Omega \times \mathbb{R}^{d \times N \times N} \rightarrow [0, \infty)$ is a continuous function with $f(x, \cdot)$ of linear…

In this paper, we consider weighted Bergman spaces $\mathcal{B}_{\alpha,p}$ of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level…

According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^N$. Given a continuous plurisubharmonic function $u$ on $\Omega$, we construct a sequence of Gaussian analytic functions $f_n$ on $\Omega$ associated with $u$ such that…

We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae have natural geometric interpretations concerning the extrinsic geometry of the round sphere.…

Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of $\mathbb{C}^{n}$ of hypersurface type. Our main result says that when a certain $1$-form on $M$ is exact on the null space of the Levi form, then the complex Green…

We express the nonlocal BMS charges of a free massless Klein-Gordon scalar field in 2+1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic…

Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…

Let $K\subset \mathbb R$ be a regular compact set and let $g(z)=g_{\overline{\mathbb C}\setminus K}(z,\infty)$ be the Green function for $\overline{\mathbb C}\setminus K$ with pole at infinity. For $\delta>0$, define $$ G(\delta):=\max\{…

We extend certain classical theorems in pluripotential theory to a class of functions defined on the support of a $(1,1)$-closed positive current $T$, analogous to plurisubharmonic functions, called $T$-plurisubharmonic functions. These…

We prove sharp near-diagonal pointwise bounds for the Green function $G_\Omega(x,y)$ for nonlocal operators of fractional order $\alpha \in (0,2)$. The novelty of our results is two-fold: the estimates are robust as $\alpha \to 2-$ and we…