The mean curvature flow in Minkowski spaces

Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we prove the short time existence and uniqueness for solutions of the mean curvature flow and prove that the flow preserves the convexity and mean convexity.We also derive some comparison principles for the mean curvature flow.

RELAXED ELASTIC LINES OF SECOND KIND ON ORIENTED SURFACE IN MINKOWSKI SPACE

The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.

Light and Entanglement Velocities for the Electron and the Proton in Minkowskian Space Require Surface Areas that Approximate the Human Cerebrum: Implications for Excess Correlations

The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The most likely candidates for the latter are the proton and the electron when related by Minkowski’s space-time. When two velocities: light in a vacuum for locality and the “entanglement” velocity based upon parameters that define the universe for non-locality, are considered the two times required to produce identities for the -v2t2 components are frequencies whose energies approximate the neutral hydrogen line (primarily associated with shifts in electron spin direction) and the mass equivalence of a proton. The values for the additional three spatial dimensions required to produce a solution whose square root is not imaginary and greater than zero are within the domains of the surface areas of the human cerebrum. Detailed calculations converge to show that the proportions of energy that represent the electron’s Compton energy and the proton’s mass equivalent may be central to the condition of excess correlation within the cerebral volume. Proton channels within the neuronal cell plasma membranes whose pH-dependent specific currents produce the required magnetic field strengths could be the physical substrates by which excess correlations between brain activities of human subjects separated by non-local distances might occur. If protons are considered as the basic Eddington (number) units of the universe then Mach’s principle that any component of the universe is determined by all of its components may be testable empirically.

Group Inverse of 2 × 2 Block Matrices over Minkowski Space M

Necessary and sufficient conditions for the existence of the group inverse of the block matrix in Minkowski Space are studied, where are both square and . The representation of this group inverse and some related additive results are also given.

The m-CMP Inverse in Minkowski Space

In this paper,a new generalized m-CMP inverse is introduced into the Minkowski space,and its related properties are discussed.Secondly,three different expressions of m-CMP inverse are listed,namely Hartwig-Spindel-bock decomposition,full-rank decomposition and integral expression.Finally,the application of the inverse m-CMP equation in solving linear equations is given.

Remarks on the Veronese Generating Submanifolds in Minkoski Space

In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkowski space are respectively space-like Minimal submanifolds of Hyperbolic space and pseudo-Rie-mannian Minimal submanifolds of pseudo-Riemannian sphere and they are of 1-type submanifolds in Minkowski space is proved.

On Quasi-Einstein Field Equation

In this paper some properties of a symmetric tensor field T（X,Y） = g（A（X）, Y） on a Riemannian manifold （M, g） without boundary which satisfies the S quasi-Einstein equation Rij-S/2gij=Tij＋bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.

Zeeman-Like Topologies in Special and General Theory of Relativity

This is a short review article in which we discuss and summarize the works of various researchers over past four decades on Zeeman topology and Zeeman-like topologies, which occur in special and general theory of relativity. We also discuss various properties and inter-relationship of these topologies.

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given number of annular ends.

Some New Translation Surfaces in 3-Minkowski Space

In this paper we study translation surfaces of some new types in 3-Minkowski space E13 and give some classifications of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.

AN APPLICATION OF RITT-WU＇S ZERO DECOMPOSITION ALGORITHM TO THE PSEUDO NULL BERTRAND TYPE CURVES IN MINKOWSKI 3-SPACE

The Bertrand curves were first studied using a computer by Wu （1987）. The same problem was studied using an improved version of Ritt-Wu＇s decomposition algorithm by Chou and Gao （1993）. This paper investigates the same problem for pseudo null Bertrand curves in Minkowski 3-space E3 1.

Curvature Estimates of Hypersurfaces in the Minkowski Space

A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.

A spin-less particle on a rotating curved surface in Minkowski space

In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.

Surface Pencil with a Common Line of Curvature in Minkowski 3-Space

In this paper, we analyze the problem of constructing a surface pencil from a given spacelie （timelike） line of curvature. Using the Frenet frame of the given line of curvature in Minkowski 3-space, we express the surface pencil as a linear combination of this frame and derive the necessary and sufficient conditions for the coefficients to satisfy the line of curvature requirement. We illustrate this method by presenting some examples.

A Kind of Rectilinear Congruences in the Minkowski 3-Space

We consider the rectilinear congruence T generated by the tangents to a one parameter family of geodesics on a space-like surface S1 in the Minkowski 3-space E13, having S1 as one of its focal surfaces. We prove that the two families of torsal surfaces of T touch the second focal surface S2 along the net of orthogonal parametric curves if and only if S1 is developable. We also obtain the necessary and sufficient condition for the correspondence between the points of S1 and S2 at the same rays preserving the...

The Extremal Surfaces in the 3-dimensional Minkowski Space

1 .Introduotion Theudy of ojnal surfaee,in Euolidean,Paoe(or other Rleman"iananifold。)has a long history.There were plen of very deop and very beautifulsults obtained byveral generations of rnathe

Spacelike Hypersurfaces of Prescribed Gauss-Kronecker Curvature in Exterior Domains

In this paper, we prove an existence theorem for spacelike convex hypersurfaces of prescribed Gauss curvature in Minkowski space.