×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Avez, A.: Essais de géométrie Riemannienne hyperbolique globale ? applications a la relativité générale. Ann. Inst. Fourier (Grenoble)13, 105-190 (1963) · Zbl 0188.54801
[2] Bancel, D.: Sur le problème de Plateau dans un varété Lorentzienne. C.R. Acad. Sci. Paris268A, 403-404 (1978) · Zbl 0381.49012
[3] Bartnik, R.: The Lorentz mean curvature equation. Thesis Melbourne 1980
[4] Calabi, E.: Examples of Bernstein problems for some non-linear equations. AMS Symposium on Global Analysis, Berkeley 1968 · Zbl 0169.53303
[5] Cheng, S.Y., Yau, S.-T.: Maximal spacelike hypersurfaces in the Lorentz-Minkowski spaces. Ann. Math.104, 407-419 (1976) · Zbl 0352.53021
[6] Eardley, D., Smarr, L.: Time functions in numerical relativity: marginally bound dust collapse. Phys. Rev. D19, 2239 (1979)
[7] Federer, H.: Geometric measure theory. Berlin, Heidelberg, New York: Springer 1969 · Zbl 0176.00801
[8] Flaherty, F.: The boundary value problem for maximal hypersurfaces. P.N.A.S. USA76, 4765-4767 (1979) · Zbl 0428.49031
[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)
[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
[13] Treibergs, A.: Entire spacelike hypersurfaces of constant mean curvature in Minkowski space. Invent. Math.66, 39-56 (1982) · Zbl 0483.53055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.