This is a preview of subscription content, log in via an institution to check access.
References
[A]Avez, A., Essais de géométrie Riemannienne hyperbolique globale — applications a la relativité générale.Ann. Inst. Fourier (Grenoble), 13 (1963), 105–190.
[AB]Audounet, J. &Bancel, D., Sets with spatial boundary and existence of submanifolds with prescribed extrinsic curvature of a Lorentzian manifold.J. Math. Pures et Appl., 60 (1981), 267–283.
[B1]Bartnik, R., Existence of maximal surfaces in asymptotically flat spacetimes.Comm. Math. Phys., 94 (1984), 155–175.
[B2]Bartnik, R., Remarks on cosmological spacetimes and constant mean curvature hypersurfaces. CMA report R38-86, to appear inComm. Math. Phys.
[B3]Bartnik, R. Maximal surfaces and general relativity, inProc. miniconf. on Analysis and Geometry ANU, June 1986. J. Hutchinson, ed.
[BS]Bartnik, R. &Simon, L., Spacelike hypersurfaces with prescribed boundary values and mean curvature.Comm. Math. Phys., 87 (1982), 131–152.
[BF]Brill, D. &Flaherty, F., Isolated maximal surfaces in spacetime.Comm. Math. Phys., 50 (1976), 157–165.
[CB]Choquet-Bruhat, Y., Spacelike submanifolds with constant mean extrinsic curvature of a Lorentzian manifold.Ann. Scuola Norm. Sup. Pisa, 3 (1976), 361–376.
[CY]Cheng, S. Y. &Yau, S. T., Maximal spacelike surfaces in Lorentz-Minkowski spaces.Ann. of Math., 104 (1976), 407–419.
[DH]Dray, T. &’t Hooft, G., The effect of spherical shells of matter on the Schwarzschild black hole.Comm. Math. Phys., 99 (1985), 613–625.
[E]Ecker, K., Area maximising hypersurfaces in Minkowski space having an isolated singularity.Manuscripta Math., 56 (1986), 375–397.
[ES]Eardley, D. &Smarr, L., Time functions in numerical relativity: Marginally bound dust collapse.Phys. Rev. D, 19 (1979), 2239–2259.
[G]Gerhardt, C.,H-surfaces in Lorentzian manifolds.Comm. Math. Phys., 89 (1983), 523–553.
[Ga]Galloway, G., Splitting theorems for spatially closed space-times.Comm. Math. Phys., 96 (1984), 423–429.
[Ge]Geroch, R., Singularities in closed universes.Phys. Rev. Lett., 17 (1966), 445–447.
[Go]Goddard, A., A generalisation of the concept of constant mean curvature and canonical time.Gen. Relativity Gravitation, 8 (1977), 525–537.
[GT]Gilbarg, D. & Trudinger, N.,Elliptic partial differential equations of second order. Springer, 1977.
[HE]Hawking, S. &Ellis, G.,The large-scale structure of space-time, Cambridge, Cambridge University Press 1973.
[K]Kobayashi, O., Maximal surfaces in the 3-dimensional Minkowski spaceL 3.Tokyo J. Math., 6 (1983), 297–309.
[MT]Marsden, J. &Tipler, F., Maximal hypersurfaces and foliations of constant mean curvature in general relativity.Phys. Rep., 66 (1980), 109–139.
[M]Morrey, C. B.,Multiple integrals in the calculus of variations. Springer, 1966.
[O]Osserman, R., A proof of the regularity everywhere of the classical solution of Plateau’s problem.Ann. of Math., 91 (1970), 550–569.
[O’N]O’Neil, B.,Semi-Riemannian geometry. Academic Press, 1984.
[Q]Quien, N., Plateau’s problem in Minkowski space.Analysis, 5 (1985), 43–60.
[T]Treibergs, A., Entire spacelike hypersurfaces of constant mean curvature in Minkowski space.Invent. Math., 66 (1982), 39–56 and inSeminar on Differential Geometry, Annals Studies 102, S.-T. Yau, ed.
[Ta]Taub, A., Spacetimes with distribution-valued curvature tensors.J. Math. Phys., 21 (1980), 1423.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bartnik, R. Regularity of variational maximal surfaces. Acta Math. 161, 145–181 (1988). https://doi.org/10.1007/BF02392297
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392297