Surfaces of annulus type with constant mean curvature in Lorentz-Minkowski space
نویسنده
چکیده
In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space L and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in L of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we characterize spacelike surfaces of revolution with constant mean curvature as the only that either i) are the solutions of the exterior Dirichlet problem for constant boundary data or ii) have an isolated conical-type singularity.
منابع مشابه
Translation Surfaces of the Third Fundamental Form in Lorentz-Minkowski Space
In this paper we study translation surfaces with the non-degenerate third fundamental form in Lorentz- Minkowski space $mathbb{L}^{3}$. As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form $III$ on the surface.
متن کاملA Weierstrass representation for linear Weingarten spacelike surfaces of maximal type in the Lorentz–Minkowski space
In this work we extend the Weierstrass representation for maximal spacelike surfaces in the 3-dimensional Lorentz–Minkowski space to spacelike surfaces whose mean curvature is proportional to its Gaussian curvature (linear Weingarten surfaces of maximal type). We use this representation in order to study the Gaussian curvature and the Gauss map of such surfaces when the immersion is complete, p...
متن کاملTimelike Surfaces of Constant Mean Curvature ±1 in Anti-de Sitter 3-space H 3 1 (−1)
It is shown that timelike surfaces of constant mean curvature ±1 in anti-de Sitter 3-space H 1 (−1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL2R via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson-Guichard correspondence, be...
متن کامل$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$
Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...
متن کامل9 Area minimization among marginally trapped surfaces in Lorentz - Minkowski space
We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same boundary values. The quintessential property of zero mean curvature surfaces in Euclidean space is that they locally minimize area with respect to their boun...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005