arXiv research

Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.

Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.

Stability of Minkowski space-time in Einstein-Yang-Mills system proven.

Proves stability of Minkowski space-time in Einstein-Yang-Mills system.

In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface consisting of a one-parameter family of spacelike submanifolds. Recently, Bousso and Randall introduced the notion of caustics of world hyper-sheets in order to define the notion of holographic domains in space-time. Here, we give a mathematica…

Proves a Minkowski inequality for static Einstein-Maxwell space-time.

In this paper, we give some characterizations for spacelike helices in Minkowski space-time. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space-time.

A minimal space-like surface in Minkowski space-time is said to be of general type if it is free of degenerate points. The fact that minimal space-like surfaces of general type in Minkowski space-time admit canonical parameters of the first (second) type implies that any minimal space-like surface is determined uniquel…

In this paper, we give the generalization of the criterion for a 3-space curve to be closed given by [3] to an n-space curve in Minkowski space-time E_v^n. Furthermore, we apply this criterion for a curve lying on an oriented surface in the Minkowski space E_v^n as an application.

The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.

We give a definition of generalized timelike Mannheim curve in Minkowski space-time $E_1^4$. The necessary and sufficient conditions for the generalized timelike Mannheim curve obtain. We show some characterizations of generalized Mannheim curve.

In this paper, the definition of generalized spacelike Mannheim curve in Minkowski space-time $E_1^4$ is given. The necessary and sufficient conditions for the generalized spacelike Mannheim curve are obtained. Also, some characterizations of Mannheim curve are given.

We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple proof of Friedrich's result on the future hyperboloidal stability of Minkowski space…

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of …

The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we i…

Proves energy estimates for tensorial wave equations, decoupling components for stability proof.

In this paper, we define a rectifying spacelike curve in the Minkowski space-time $E_1^4$ as a curve whose position vector always lies in orthogonal complement $N^{\bot}$ of its principal normal vector field $N$. In particular, we study the rectifying spacelike curves in $E_1^4$ and characterize such curves in terms of…

In this paper, we study the Lorentzian minimal surfaces in the Minkowski space-time with finite type Gauss map. First, we obtain the classification of this type of surfaces with pointwise 1-type Gauss map. Then, we proved that there are no Lorentzian minimal surface in the Minkowski space-time with null 2-type Gauss ma…

In this paper, we establish equiform differential geometry of space and timelike curves in 4-dimensional Minkowski space. We obtain some conditions for these curves. Also, general helices with respect to their equiform curvatures are characterized.

In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with …

The tangent hyperplanes of the "manifolds" of this paper equipped a so-called Minkowski product. It is neither symmetric nor bilinear. We give a method to handing such an object as a locally hypersurface of a generalized space-time model and define the main tools of its differential geometry: its fundamental forms, its…

Extends Minkowski stability proof to minimal decay assumptions.

This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds (an investigation initiated by Gibbons-Ishibashi). Specifically, we study geodesic connectedness. We give geometric-topological proofs of geodesic connectedness for classes of space-times to which kno…

The paper examines stability of Minkowski inequalities in warped product spaces.

Locally symplectic structure found on Kerr space-time.

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification o…

New method creates vacuum data at minimal and borderline decay thresholds.

The hyperbolic space $ \H^d$ can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $Γ$ is a group of linear isometries of the Minkowski space such that $\H^d/Γ$ is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, g…

The paper examines the stability of Minkowski inequality for nearly spherical domains.

Explains basics of supersymmetry and supergeometry.

In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum solutions are established at the same time. In particular, the map from Cauchy int…

Researchers found sub-Lorentzian geodesics on a specific Lie subgroup.

New proof of Minkowski spacetime stability in exterior regions.

We show that supersymmetric M-theory compactifications to three-dimensional Minkowski space-time preserving $\mathcal{N}=2$ supersymmetry allow for a class of internal manifolds more general than the Calabi-Yau one, namely the class of locally conformally Kähler manifolds which locally carry a preferred Calabi-Yau stru…

A survey on the recent work of Danciger, Guéritaud and Kassel on Margulis space-times and complete anti-de Sitter space-times. Margulis space-times are quotients of the 3-dimensional Minkowski space by (non-abelian) free groups acting propertly discontinuously. Goldman, Labourie and Margulis have shown that they are de…

Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.

Submanifolds in Lorentz-Minkowski space are investigated from various mathematical viewpoints and are of interest also in relativity theory. We define the hyperbolic surface and the de Sitter surface of a curve in the spacelike hypersurface M in the Minkowski 4-space. These surfaces are respectively located in the hype…

Proves stability of Minkowski space for specific initial data.

Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the energy-momentum tensor of a massive spin 1/2 particle is shown.

The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface and should be independent of whichever space-like region it bounds. An impor…

Extends particle classification to curved space-times using groupoids.

Survey on stability of Minkowski spacetime in relativity.

Extends global stability of Minkowski spacetime to minimal decay assumptions.

New stability theorem for hypersurfaces in Minkowski spaces.

New proof of injectivity for broken non-abelian X-ray transform in Minkowski space.

The paper derives new inequalities on manifolds and applies them to convex hypersurfaces.

In this paper, we illustrated one scenario to modify the Ivanenko-Landau-Kähler equation. Since Ivanenko and Landau introduced the equation in 1928, the equation has been regarded as having a certain role as a fermion in particular in the discrete Lattice. Also, although it correctly is formulated as an alternative cla…

We prove existence and stability of smooth entire strictly convex spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space. The proof is based on barrier constructions and local a priori estimates.