Some rigidity results for spatially closed spacetimes
Banach Center Publications (1997)
- Volume: 41, Issue: 1, page 21-34
- ISSN: 0137-6934
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topGalloway, Gregory. "Some rigidity results for spatially closed spacetimes." Banach Center Publications 41.1 (1997): 21-34. <http://eudml.org/doc/252242>.
@article{Galloway1997,
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 = {http://eudml.org/doc/252242},
volume = {41},
year = {1997},
}
TY - JOUR
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 - http://eudml.org/doc/252242
ER -
References
top- [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
- [AH] L. Andersson and R. Howard, Rigidity results for Robertson-Walker and related spacetimes, preprint.
- [B1] R. Bartnik, Regularity of variational maximal surfaces, Acta Mathematica 161 (1988), 145-181. Zbl0667.53049
- [B2] R. Bartnik, Remarks on cosmological spacetimes and constant mean curvature surfaces, Commun. Math. Phys. 117 (1988), 615-624. Zbl0647.53044
- [BEE] J.K. Beem, P.E. Ehrlich, K.L. Easley, Global Lorentzian Geometry, 2nd ed., Marcel Dekker, New York, 1996.
- [BF] D. Brill and F. Flaherty, Isolated maximal hypersurfaces in spacetime, Commun. Math. Phys. 50 (1976), 157-165. Zbl0337.53051
- [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
- [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
- [EhG] P. Ehrlich and G.J. Galloway, Timelike lines, Classical and Quantum Grav. J. (1990), 297-307.
- [E1] J.-H. Eschenburg, Local convexity and nonnegative curvature - Gromov's proof of the sphere theorem, Invent. Math. 84 (1986), 507-522. Zbl0594.53034
- [E2] J.-H. Eschenburg, The splitting theorem for spacetimes with strong energy condition, J. Diff. Geom. 27 (1988), 477-491. Zbl0647.53043
- [E3] J.-H. Eschenburg, Maximum principles for hypersurfaces, Manuscripta Math. 64 (1989), 55-75.
- [EG] J.-H. Eschenburg and G.J. Galloway, Lines in spacetimes, Comm. Math. Phys. 148 (1992), 209-216. Zbl0756.53028
- [F] T. Frankel, On the fundamental group of a comapct minimal submanifold, Ann. Math. 83 (1966), 68-73. Zbl0189.22401
- [G1] G.J. Galloway, Splitting theorems for spatially closed space-times, Commun. Math. Phys. 96 (1984), 423-429. Zbl0575.53040
- [G2] G.J. Galloway, The Lorentzian splitting theorem without completeness assumption, J. Diff.Geom. 29 (1989), 373-387. Zbl0667.53048
- [G3] G.J. Galloway, Some connections between global hyperbolicity and geodesic completeness, J. Geom. Phys. 6 (1989), 127-141. Zbl0677.53071
- [GH] G.J. Galloway and A. Horta, Regularity of Lorentzian Busemann functions, Trans. Amer. Math. Soc. 348 (1996), 2063-2084. Zbl0858.53052
- [GC] C. Gerhardt, H-surfaces in Lorentzian manifolds, Commun. Math. Phys. 89 (1983), 523-553. Zbl0519.53056
- [GR1] R. Geroch, Singularities in closed universes, Phys. Rev. Lett. 17 (1966), 445-447. Zbl0142.24007
- [GR2] R. Geroch, Singularities, in: Relativity, M. Carmeli, S. Fickler and L. Witten (eds.), Plenum Press, New York, 1970, 259-291.
- [GT] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations, 2nd ed., Springer-Verlag, New York, 1983.
- [HE] S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge, 1973. Zbl0265.53054
- [I] R. Ichida, Riemannian manifolds with compact boundary, Yokohama Math. J. 29 (1981), 169-177. Zbl0493.53033
- [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
- [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
- [S] R. Schoen, Uniqueness, symmetry and embeddedness of minimal surfaces, J. Diff. Geom. 18 (1983), 791-804. Zbl0575.53037
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