arXiv research

Paper generalizes Minkowski inequality for umbilical hypersurfaces with free boundary.

Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…

A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% {YuFu2014GCRS} into the Min…

The paper generalizes Bour's theorem to Minkowski 4-space.

Study smooth hypersurfaces with prescribed curvature in Minkowski space.

Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…

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.

Derives exact formula for Minkowski sum of ellipsoids in N-space.

Classifies timelike translating solitons in Minkowski space.

Solves a generalized dual Minkowski problem for specific values of q.

We apply Garnier's method to solve the Plateau problem for maximal surfaces in Minkowski 3-space. Our study relies on the improved version we gave of R. Garnier's resolution of the Plateau problem for polygonal boundary curves in Euclidean 3-space. Since in Minkowski space the method does not allow us to avoid the exis…

Study bifurcations of curves on surfaces in Minkowski 3-space.

Study of timelike surfaces in Minkowski space with specific geometric properties.

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…

Developed a sub-Riemannian version of Minkowski problem in Heisenberg groups.

The paper classifies maximal translation surfaces in Lorentz-Minkowski space.

Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.

Study of spatial curves in generalized Minkowski spaces.

Develops Brunn-Minkowski theory in hyperbolic space using hyperbolic p-sum.

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 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…

The paper studies Gauss maps of space-like stationary surfaces in Lorentz-Minkowski space, focusing on ramification and unicity.

The classical Minkowski problem in Minkowski space asks, for a positive function $φ$ on $\mathbb{H}^d$, for a convex set $K$ in Minkowski space with $C^2$ space-like boundary $S$, such that $φ(η)^{-1}$ is the Gauss--Kronecker curvature at the point with normal $η$. Analogously to the Euclidean case, it is possible to f…

Proves inequality for maximal spacelike submanifolds in Minkowski space.

Paper solves Christoffel-Minkowski problem in hyperbolic space.

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space.

Paper studies singularities of timelike minimal surfaces in Minkowski 3-space.

A world sheet in Lorentz-Minkowski space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds in Lorentz-Minkowski space. In this paper we investigate differential geometry of world sheets in Lorentz-Minkowski space as an application of the theory of big wave fronts.

The paper classifies isoparametric hypersurfaces in conic Finsler spaces.

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.

We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on the Minkowski space which ar…

In this note we apply the general Reilly formula established in \cite{QX} to the solution of a Neumann boundary value problem to prove an optimal Minkowski type inequality in space forms.

The study finds hypersurfaces with constant scalar curvature in Minkowski space.

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.

Study on curvature flow in Minkowski space for cocompact hypersurfaces.

General $(α, β)$ norms are an important class of Minkowski norms which contains the original $(α, β)$ norms. In this note, by studying the behavior of the Darboux curves of the indicatrix, we give a characterization of 3-dimensional general $(α, β)$ norms. By studying the isoperimetric properties of the indicatrix, as …

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

Compactifies Minkowski space using unitary matrices.

We obtain isometric minimal helicoidal and rotational surfaces using generalized Bour's theorem in three dimensional Minkowski space. In addition, we show that the surfaces preserve minimality when their Gauss maps identically equal, choosing any diffentiable functions on the profile curve.

Study translating solitons in Minkowski space with prescribed Gauss image.

Study on maximal surfaces with high genus in Lorentz-Minkowski space.

Sharp Minkowski inequality found for AdS-Melvin spacetime surfaces.

Proves equality in Minkowski inequality for static, flat manifolds.

Investigates differences in solving mean curvature problems in Euclidean and Lorentz-Minkowski spaces.

Maximal surfaces in Lorentz-Minkowski space have conjugate graphs.

The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose novel statistical symmetric distances based on the Minkowski's inequality for probability densities belonging to Lebesgue spaces. These statistical Minkowski distances admit closed…

Survey Bernstein-type theorems for graphical surfaces in Euclidean and Lorentz-Minkowski spaces.

Solves capillary $L_p$-Christoffel-Minkowski problem in half-space.