Related papers: Green functions on stationary varifolds
We discuss approximations of the Riemannian geometry near the horizon. If a D+1 dimensional manifold N has a bifurcate Killing horizon then we approximate N by a product of the two-dimensional Rindler space and a D-1 dimensional Riemannian…
A compact form for the static Green's function for symmetric loading of an elastic sphere is derived. The expression captures the singularity in closed form using standard functions and quickly convergent series. Applications to problems…
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
We consider Euler flows on two-dimensional (2D) periodic domain and are interested in the stability, both linear and nonlinear, of a simple equilibrium given by the 2D Taylor-Green vortex. As the first main result, numerical evidence is…
An earlier contour expression for the Green function of a free complex scalar field in the presence of a conical singularity with localised magnetic flux is shown to yield expressions for the field correlator and defect block expansions…
We solve for the retarded Greens function for linearized gravity in a background with a negative cosmological constant, anti de Sitter space. In this background, it is possible for a signal to reach spatial infinity in a finite time.…
A nonperturbative method to obtain on- and off-site one-particle Green's function is introduced and applied to noninteracting Hubbard model with next nearest neighbor hopping and interacting Hubbard model in large dimensions, for example.…
A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck…
We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, and satisfy the equation $\Delta f…
We prove that the number of critical points of a Li-Tam Green's function on a complete open Riemannian surface of finite type admits a topological upper bound, given by the first Betti number of the surface. In higher dimensions, we show…
For a scalar CFT with a monodromy defect, a `subtracted Green function' is derived in terms of an Appell $F_1$ function. A conjectured relation of Gimenez-Grau and Liendo is thereby proved and extended and shown to hold for generalised free…
There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we…
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole spacetime, i.e., a $(1+d)$-spacetime with $d\geq3$ which presents a solid angle deficit. Our result is…
This is a sequel to arXiv:2401.02087. We prove the Green function rigidity conjecture in arXiv:2401.02087 for conformal Laplacian in dimension $n\geq 3$. For the Paneitz operator, we prove the Green function rigidity conjecture when $n\neq…
We consider the asymptotic behaviour of the Chern-Simons Green's function of the $\nu=1/\tilde{\phi}$ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the…
The Lempert function for a set of poles in a domain of $\mathbb C^n$ at a point $z$ is obtained by taking a certain infimum over all analytic disks going through the poles and the point $z$, and majorizes the corresponding multi-pole…
We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincar\'e inequality. In the process, a sharp decay estimate for the minimal positive Green's function is obtained. This…
We study the spatial asymptotics of Green's function for the 1d Schrodinger operator with operator-valued decaying potential. The bounds on the entropy of the spectral measures are obtained. They are used to establish the presence of a.c.…
In this paper, we consider a weakly coupled system of nonlocal operators which contain both diffusion part with uniformly elliptic diffusion matrices and bounded drift vectors and the jump part with relatively general jump kernels. We use…