Space-like surfaces in an anti-de Sitter space
Nous passons en revue certains résultats récents sur l’existence et l’unicité des sphères à courbure moyenne constante dans les variétés riemanniennes homogènes simplement connexes de dimension et leurs liens avec le problème isopérimétrique dans ces variétés.
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
We prove the existence of many constant mean curvature surfaces of revolution with two ends which are immersed or embedded in hyperbolic space. We also study their stability.
In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.