Convexity of the solutions to the constant mean curvature spacelike surface equation in the Lorentz-Minkowski space

被引：6

作者：

Albujer, Alma L. ^{[1
]}

Caballero, Magdalena ^{[1
]}

Lopez, Rafael ^{[2
]}

机构：

[1] Univ Cordoba, Dept Matemat, E-14071 Cordoba, Spain

[2] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 258卷 / 07期

关键词：

Spacelike hypersurface; Constant mean curvature; Dirichlet problem; Convex curve; Strictly convex surface; HYPERSURFACES;

D O I：

10.1016/j.jde.2014.12.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a spacelike graph of constant mean curvature H not equal 0 in the 3-dimensional Lorentz-Minkowski space over a bounded domain with pseudo-elliptic boundary is strictly convex. By a pseudoelliptic curve we mean a closed and planar curve which intersects any branch of any hyperbola at most at five points. We also provide an example that shows that we cannot remove the assumption on the boundary being a pseudo-elliptic curve. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：2364 / 2374

页数：11

共 24 条

[1] On the curvatures of bounded complete spacelike hypersurfaces in the Lorentz-Minkowski space [J].