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Title

Some rigidity results for spatially closed spacetimes

Authors 1

Affiliations

  1. Department of Mathematics and Computer Science , University of Miami, Coral Gables, FL 33124, U.S.A.

Bibliography

  1. [AGH] L. Andersson, G.J. Galloway, and R. Howard, A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian geometry, preprint.
  2. [AH] L. Andersson and R. Howard, Rigidity results for Robertson-Walker and related spacetimes, preprint.
  3. [B1] R. Bartnik, Regularity of variational maximal surfaces, Acta Mathematica 161 (1988), 145-181.
  4. [B2] R. Bartnik, Remarks on cosmological spacetimes and constant mean curvature surfaces, Commun. Math. Phys. 117 (1988), 615-624.
  5. [BEE] J.K. Beem, P.E. Ehrlich, K.L. Easley, Global Lorentzian Geometry, 2nd ed., Marcel Dekker, New York, 1996.
  6. [BF] D. Brill and F. Flaherty, Isolated maximal hypersurfaces in spacetime, Commun. Math. Phys. 50 (1976), 157-165.
  7. [B+] R. Budic, J. Isenberg, L. Lindblom and P.B. Yasskin, On the determination of Cauchy surfaces from intrinsic properties, Comm. Math. Phys. 61 (1978), 87-95.
  8. [C] E. Calabi, An extension of E. Hopf's maximum principle with applications to Riemannian geometry, Duke Math. J. 25 (1957), 45-56.
  9. [EhG] P. Ehrlich and G.J. Galloway, Timelike lines, Classical and Quantum Grav. J. (1990), 297-307.
  10. [E1] J.-H. Eschenburg, Local convexity and nonnegative curvature - Gromov's proof of the sphere theorem, Invent. Math. 84 (1986), 507-522.
  11. [E2] J.-H. Eschenburg, The splitting theorem for spacetimes with strong energy condition, J. Diff. Geom. 27 (1988), 477-491.
  12. [E3] J.-H. Eschenburg, Maximum principles for hypersurfaces, Manuscripta Math. 64 (1989), 55-75.
  13. [EG] J.-H. Eschenburg and G.J. Galloway, Lines in spacetimes, Comm. Math. Phys. 148 (1992), 209-216.
  14. [F] T. Frankel, On the fundamental group of a comapct minimal submanifold, Ann. Math. 83 (1966), 68-73.
  15. [G1] G.J. Galloway, Splitting theorems for spatially closed space-times, Commun. Math. Phys. 96 (1984), 423-429.
  16. [G2] G.J. Galloway, The Lorentzian splitting theorem without completeness assumption, J. Diff.Geom. 29 (1989), 373-387.
  17. [G3] G.J. Galloway, Some connections between global hyperbolicity and geodesic completeness, J. Geom. Phys. 6 (1989), 127-141.
  18. [GH] G.J. Galloway and A. Horta, Regularity of Lorentzian Busemann functions, Trans. Amer. Math. Soc. 348 (1996), 2063-2084.
  19. [GC] C. Gerhardt, H-surfaces in Lorentzian manifolds, Commun. Math. Phys. 89 (1983), 523-553.
  20. [GR1] R. Geroch, Singularities in closed universes, Phys. Rev. Lett. 17 (1966), 445-447.
  21. [GR2] R. Geroch, Singularities, in: Relativity, M. Carmeli, S. Fickler and L. Witten (eds.), Plenum Press, New York, 1970, 259-291.
  22. [GT] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations, 2nd ed., Springer-Verlag, New York, 1983.
  23. [HE] S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge, 1973.
  24. [I] R. Ichida, Riemannian manifolds with compact boundary, Yokohama Math. J. 29 (1981), 169-177.
  25. [K] A. Kasue, Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary, J. Math. Soc. Japan, 35 (1983), 117-131.
  26. [N] R.P.A.C. Newman, A proof of the splitting conjecture of S.-T. Yau, J. Diff. Geom. 31 (1990), 163-184.
  27. [S] R. Schoen, Uniqueness, symmetry and embeddedness of minimal surfaces, J. Diff. Geom. 18 (1983), 791-804.
Banach Center Publications
1997/41/1
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Pages:
21-34
Main language of publication
English
Published
1997
Exact and natural sciences