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Spacelike hypersurfaces with prescribed boundary values and mean curvature. (English) Zbl 0512.53055


MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
49Q05 Minimal surfaces and optimization
35Q99 Partial differential equations of mathematical physics and other areas of application
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[9] Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0361.35003
[10] Marsden, J., Tipler, F.: Maximal hypersurfaces and foliations of constant mean curvature in general relativity. Phys. Rep.66, 109-139 (1980) · doi:10.1016/0370-1573(80)90154-4
[11] Morrey, C.B.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0142.38701
[12] Michael, J., Simon, L.: Sobolev and mean-value inequalities on generalized submanifolds of IR?. Commun. Pure Appl. Math.26, 361-379 (1973) · Zbl 0256.53006 · doi:10.1002/cpa.3160260305
[13] Treibergs, A.: Entire spacelike hypersurfaces of constant mean curvature in Minkowski space. Invent. Math.66, 39-56 (1982) · Zbl 0483.53055 · doi:10.1007/BF01404755
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