相关论文: Boost Invariant Surfaces with Pointwise 1-Type Gau…
It is known that self-duality equations for multi-instantons on a line in four dimensions are equivalent to minimal surface equations in three dimensional Minkowski space. We extend this equivalence beyond the equations of motion and show…
In this article we introduce new affinely invariant points---`special parabolic points'---on the parabolic set of a generic surface $M$ in real 4-space, associated with symmetries in the 2-parameter family of reflexions of $M$ in points of…
We define a categorical birational invariant for minimal geometrically rational surfaces with a conic bundle structure over a perfect field via components of a natural semiorthogonal decomposition. Together with the similar known result on…
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…
In this work we study the relativistic kinetic theory of a boost-invariant conformal gas on a static, maximally symmetric background $dS_3\times \mathbb{R}$, considering all constant-curvature slicings of $dS_3$ - flat, spherical, or…
In this study, we deal with the Gauss map of tubular hypersurfaces in 4-dimensional Lorentz-Minkowski space concerning the linearized operators $\mathcal{L}_{1}$ (Cheng-Yau) and $\mathcal{L}_{2}$. We obtain the $\mathcal{L}_{1}$ (Cheng-Yau)…
Canonical principal parameters are introduced for surfaces in $\mathbb R^3$ without umbilical points. It is proved that in these parameters the surface is determined (up to position in space) by a pair of invariants satisfying a partial…
We are concerned with spacelike convex hypersurfaces of positive constant (K-hypersurfaces) or prescribed Gauss curvature in Minkowski space. Our main purpose is to study entire solutions as well as the Dirichlet problem in bounded domains…
We study nonorientable maximal surfaces in Lorentz-Minkowski 3-space. We prove some existence results for surfaces of this kind with high genus and one end.
In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space $\l^3$ and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational…
The Gauss map $g$ of a surface $\Sigma$ in $\mathbb{R}^4$ takes its values in the Grassmannian of oriented 2-planes of $\mathbb{R}^4$: $G^+(2,4)$. We give geometric criteria of stability for minimal surfaces in $\mathbb{R}^4$ in terms of…
In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces…
We prove that the Gauss curvature and the curvature of the normal connection of any minimal surface in the four dimensional Euclidean space satisfy an inequality, which generates two classes of minimal surfaces: minimal surfaces of general…
We study the formation of marginally trapped surfaces in the head-on collision of two shock waves both in anti-de Sitter and Minkowski space-time in various dimensions as a function of the spread of the energy density in transverse space.…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…
In this paper, we prove effective estimates for the number of exceptional values and the totally ramified value number for the Gauss map of pseudo-algebraic minimal surfaces in Euclidean four-space and give a kind of unicity theorem.
In this paper, we study meridian surfaces of Weingarten type in Euclidean 4-space E^4. We give the neccessary and sufficient conditions for a meridian surface in E^4 to become Weingarten type.
We study the properties of the loosely trapped surface (LTS) and the dynamically transversely trapping surface (DTTS) in Einstein-Maxwell systems. These concepts of surfaces were proposed by the four of the present authors in order to…
In the present paper we study normal transport surfaces in four-dimensional Euclidean space $\mathbb{E}^{4}$ which are the generalization of surface offsets in $\mathbb{E}^{3}$. We find some results of normal transport surfaces in…