Surfaces of prescribed mean curvature vector in semi-Riemannian manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Bergner, Matthias¹  Schaefer, Lars¹ 

[1] Leibniz Univ Hannover, Inst Differentialgeometrie, D-30167 Hannover, Germany

关键词: Prescribed mean curvature;    Quasilinear initial value problem;    Hyperbolic system;   

DOI  :  10.1016/j.jmaa.2012.05.004

来源: Elsevier

【 摘 要 】

Solving a second order, quasilinear initial value problem, we prove existence and uniqueness of both space-like and time-like immersions of prescribed mean curvature vector in general semi-Riemannian manifolds. Such surfaces arise for example as critical points of generalized area functionals as well as self-similar solutions of the mean curvature flow. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free