Geodesic
Criteria of instability of surfaces of zero mean curvature in warped Lorentz products
Sbornik. Mathematics, Tome 187 (1996) no. 11, pp. 1643-1663

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In this paper we investigate the stability of surfaces of zero mean curvature in Lorentz manifolds. In the case when the enveloping manifold is a warped Lorentz product and under certain assumptions about the warping function, it is proved that every stable minimal tube or strip is a totally geodesic manifold. 
@article{SM_1996_187_11_a2,
     author = {V. A. Klyachin and V. M. Miklyukov},
     title = {Criteria of instability of surfaces of zero mean curvature in warped {Lorentz} products},
     journal = {Sbornik. Mathematics},
     pages = {1643--1663},
     publisher = {mathdoc},
     volume = {187},
     number = {11},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_11_a2/}
}
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V. A. Klyachin; V. M. Miklyukov. Criteria of instability of surfaces of zero mean curvature in warped Lorentz products. Sbornik. Mathematics, Tome 187 (1996) no. 11, pp. 1643-1663. http://geodesic.mathdoc.fr/item/SM_1996_187_11_a2/