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Deformations of stationary surfaces. (English) Zbl 0891.53043

Authors’ abstract: “We show that a spacelike surface with zero mean curvature in a Lorentzian 4-manifold satisfying the null convergence condition is locally a stable minimum for the area functional when compared with nearby surfaces having isotropic (null) mean curvature vector”.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
49Q05 Minimal surfaces and optimization
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
49Q20 Variational problems in a geometric measure-theoretic setting
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