相关论文: Ghost points in inverse scattering constructions o…
We prove a removable singularities theorem for point singularities of the coupled yang mills fermion equations, on a bundle over a two dimensional base space.
We study the removability of a singular set for elliptic equations involving weight functions and variable exponents. We consider the case where the singular set satisfies conditions related to some generalization of upper Minkowski content…
We study static spherically symmetric solutions to Einstein's equations with a repulsive singularity at the centre. We show that geodesics are extendible across the singularity, so the singularity does not lead to pathological causality…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
We study the removable singularity problem for $(-1)$-homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We prove that any local $(-1)$-homogeneous solution $u$ near a…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…
In this paper, we study an inverse scattering problem at fixed energy on three-dimensional asymptotically hyperbolic St{\"a}ckel manifolds having the topology of toric cylinders and satisfying the Robertson condition. On these manifolds the…
The inverse scattering theory for the sine-Gordon equation discretized in space and both in space and time is considered.
Singular spacetimes are a natural prediction of Einstein's theory. Most memorable are the singular centers of black holes and the big bang. However, dilatonic extensions of Einstein's theory can support nonsingular spacetimes. The…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
Local solutions are a vivid and long-living topic in gravitational physics. We consider exact static pseudo-spherically symmetric solutions of semi-classical Einstein's equations in presence of the trace anomaly contribution. We investigate…
We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of…
We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
We consider vacuum metrics admitting conformal compactification which is smooth up to the scri $\mathscr{I^+}$. We write metric in the Bondi-Sachs form and expand it into power series in the inverse affine distance $1/r$. Like in the case…