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Entire spacelike hypersurfaces of constant mean curvature in Minkowski space. (English) Zbl 0483.53055

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
35J67 Boundary values of solutions to elliptic equations and elliptic systems
83C99 General relativity
Citations:
Zbl 0352.53021
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References:
[1] Bancel, D.: Sur le problème de Plateau dans une variété lorentzienne. C.R. Acad. Sci. Paris.286A, 403-404 (1978) · Zbl 0381.49012
[2] Bartnik, R.: The Lorentz mean curvature equation. University of Melbourne: Masters Thesis 1980
[3] Bombieri, E.: Theory of Minimal Surfaces and a counterexample to the Bernstein conjecture in high dimensions. Courant Institute Lecture Notes 1970
[4] Calabi, E.: Examples of Bernstein problems for some nonlinear equations. Proc. Symp. Pure Appl. Math.,15, 223-230 (1968)
[5] Cheng, S.-Y., Yau, S.-T.: Maximal spacelike hypersurfaces in the Lorentz-Minkowski spaces. Ann. of Math.104, 407-419 (1976) · Zbl 0352.53021
[6] Cheng, S.-Y., Yau, S.-T.: Differential equations on Riemannian manifolds and their geometric applications. Comm. Pure Appl. Math.,28, 337-354 (1975) · Zbl 0312.53031
[7] Chern, S.-S.: Minimal submanifolds in a Reimannian manifold. University of Kansas: Notes 1968
[8] Choquet-Bruhat, Y.: Maximal submanifolds and submanifolds of constant extrinsic curvature. Ann. Scoula Norm. Sup. Pisa.3, 361-376 (1976) · Zbl 0332.53035
[9] Flaherty, F.: The boundary value problem for maximal hypersurfaces. Proc. Nat. Acad. Sci. USA, 76,10, 4765-4767 (1979) · Zbl 0428.49031
[10] Gilbarg, D., Trudinger, N.: Elliptic Partial differential equations of second order. Berlin Heidelberg New York: Springer Verlag 1977 · Zbl 0361.35003
[11] Giusti, E.: On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions. Invent. Math.46, 111-136 (1978) · Zbl 0381.35035
[12] Goddard, A.: Some remarks on the existence of spacelike hypersurfaces of constant mean curvature. Math. Proc. Cambridge philos. Soc.82, 489-495 (1977) · Zbl 0386.53042
[13] Marsden, J., Tipler, F.: Maximal hypersurfaces and foliations of constant mean curvature in general relativity. Phys. Rev. Lett. 1980
[14] Shiffman, M.: On the existence of subsonic flows of a compressible fluid. J. Rational Mech. Anal.,1, 605-652 (1952) · Zbl 0048.19301
[15] Sibner, L.M., Sibner, R.J.: A nonlinear Hodge-de Rham theorem. Acta Math.125, 57-73 (1970) · Zbl 0216.45703
[16] Stumbles, S.: Hypersurfaces of constant mean extrinsic curvature. Annals of Physics133, 28-56 (1980) · Zbl 0472.53063
[17] Treibergs, A.: Entire spacelike hypersurfaces of constant mean curvature in Minkowski space. Doctoral dissertation University: Stanford 1980 · Zbl 0483.53055
[18] Yau, S.-T.: Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math.,28, 201-228 (1975) · Zbl 0297.31005
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