Related papers: Null hypersurfaces as wave fronts in Lorentz-Minko…
The pinched/non-pinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to…
A general integral inequality is established for compact spacelike submanifolds of codimension two in the Lorentz-Minkowski spacetime under the assumption that the mean curvature vector field is parallel. This inequality is then used to…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
We study the influence of the existence of totally geodesic null hypersurface on the properties of a Lorentzian manifold. By coupling the rigging technique with the existence of a null foliation we prove the existence of a Riemann flow…
In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a non-null ruled surface to be a slant ruled surface in E_1^3. Moreover,…
A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can…
We consider convex spacelike polyhedra oriented in Minkowski space. These are the classical analogues of spinfoam intertwiners. We point out a parametrization of these shapes using null face normals, with no constraints or redundancies. Our…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…
In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with $P+aH=b$ in a locally symmetric Lorentz space $L_{1}^{n+1}$. Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in…
In this paper, we prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations. Spacelike-characteristic initial data are posed on a compact 3-disk and…
In this paper, the pinching problems of complete $\lambda$-hypersurfaces in a Euclidean space $\mathbb R^{n+1}$ are studied. By making use of the Sobolev inequality, we prove a global pinching theorem of complete $\lambda$-hypersurfaces in…
We consider the global evolution problem for Einstein's field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field evolving under its own gravitational field. We establish the existence of a…
Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming wavefront. In optical metasurfaces, for example, the localized modes of individual meta-units govern the wavefront shape over a broad…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
A unified algebraic construction of the classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions for the…
The purpose of this paper is to study complete $\lambda$-surfaces in Euclidean space $\mathbb R^3$. A complete classification for 2-dimensional complete $\lambda$-surfaces in Euclidean space $\mathbb R^3$ with constant squared norm of the…
The authors study the geometry of lightlike hypersurfaces on a four-dimensional manifold $(M, c)$ endowed with a pseudoconformal structure $c = CO (2, 2)$. They prove that a lightlike hypersurface $V \subset (M, c)$ bears a foliation formed…
We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly Lorentz-invariant completeness relation (resolution of…
In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are translating solitons for the inverse mean curvature flow. In particular, we prove the existence of non-cylindrical ruled…
The 2-surface characterization of special classical radiative Higgs-, Yang-Mills and linear zero-rest-mass (l.z.r.m) fields with any spin is investigated. We determine all the zero quasi-local mass Higgs- and Yang-Mills field configurations…