Some rigidity results for spatially closed spacetimes

Gregory Galloway

Banach Center Publications (1997)

  • Volume: 41, Issue: 1, page 21-34
  • ISSN: 0137-6934

How to cite


Galloway, Gregory. "Some rigidity results for spatially closed spacetimes." Banach Center Publications 41.1 (1997): 21-34. <>.

author = {Galloway, Gregory},
journal = {Banach Center Publications},
keywords = {Cauchy surface; energy condition; geodesic completeness; mean curvature; rigidity; hypersurfaces; space-times; maximum principle; splitting},
language = {eng},
number = {1},
pages = {21-34},
title = {Some rigidity results for spatially closed spacetimes},
url = {},
volume = {41},
year = {1997},

AU - Galloway, Gregory
TI - Some rigidity results for spatially closed spacetimes
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 1
SP - 21
EP - 34
LA - eng
KW - Cauchy surface; energy condition; geodesic completeness; mean curvature; rigidity; hypersurfaces; space-times; maximum principle; splitting
UR -
ER -


  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. Zbl0935.35020
  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. Zbl0667.53049
  4. [B2] R. Bartnik, Remarks on cosmological spacetimes and constant mean curvature surfaces, Commun. Math. Phys. 117 (1988), 615-624. Zbl0647.53044
  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. Zbl0337.53051
  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. Zbl0403.53030
  8. [C] E. Calabi, An extension of E. Hopf's maximum principle with applications to Riemannian geometry, Duke Math. J. 25 (1957), 45-56. Zbl0079.11801
  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. Zbl0594.53034
  11. [E2] J.-H. Eschenburg, The splitting theorem for spacetimes with strong energy condition, J. Diff. Geom. 27 (1988), 477-491. Zbl0647.53043
  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. Zbl0756.53028
  14. [F] T. Frankel, On the fundamental group of a comapct minimal submanifold, Ann. Math. 83 (1966), 68-73. Zbl0189.22401
  15. [G1] G.J. Galloway, Splitting theorems for spatially closed space-times, Commun. Math. Phys. 96 (1984), 423-429. Zbl0575.53040
  16. [G2] G.J. Galloway, The Lorentzian splitting theorem without completeness assumption, J. Diff.Geom. 29 (1989), 373-387. Zbl0667.53048
  17. [G3] G.J. Galloway, Some connections between global hyperbolicity and geodesic completeness, J. Geom. Phys. 6 (1989), 127-141. Zbl0677.53071
  18. [GH] G.J. Galloway and A. Horta, Regularity of Lorentzian Busemann functions, Trans. Amer. Math. Soc. 348 (1996), 2063-2084. Zbl0858.53052
  19. [GC] C. Gerhardt, H-surfaces in Lorentzian manifolds, Commun. Math. Phys. 89 (1983), 523-553. Zbl0519.53056
  20. [GR1] R. Geroch, Singularities in closed universes, Phys. Rev. Lett. 17 (1966), 445-447. Zbl0142.24007
  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. Zbl0265.53054
  24. [I] R. Ichida, Riemannian manifolds with compact boundary, Yokohama Math. J. 29 (1981), 169-177. Zbl0493.53033
  25. [K] A. Kasue, Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary, J. Math. Soc. Japan, 35 (1983), 117-131. Zbl0494.53039
  26. [N] R.P.A.C. Newman, A proof of the splitting conjecture of S.-T. Yau, J. Diff. Geom. 31 (1990), 163-184. Zbl0695.53049
  27. [S] R. Schoen, Uniqueness, symmetry and embeddedness of minimal surfaces, J. Diff. Geom. 18 (1983), 791-804. Zbl0575.53037

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.