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Maximal tubes and bands in Minkowski space. (English. Russian original) Zbl 0801.53042

Russ. Acad. Sci., Sb., Math. 77, No. 2, 427-453 (1994); translation from Mat. Sb. 183, No. 12, 45-76 (1992).
Summary: Spacelike surfaces of zero mean curvature in Minkowski space are considered, and finite time conditions for the existence of tubes and bands of codimension 1 are given. For two-dimensional bands of arbitrary codimension, the bounds of admissible rate of exit to a hypersurface are indicated, and some information on the number of branchings is presented. A distinctive feature of the work is the use in estimates, as a basic characteristic of a surface, of the local time flow through sections of a tube or a band.

MSC:

53C40 Global submanifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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