On the mean curvature of spacelike hypersurfaces in spatially parabolic GRW spacetimes

Authors

  • Ning Zhang School of Science, Henan Institute of Technology

DOI:

https://doi.org/10.24297/jam.v25i.9897

Keywords:

Parabolic, Uniqueness, GRW spacetimes, Mean curvature, Spacelike hypersurface

Abstract

Several uniqueness results for complete spacelike hypersurfaces in Generalized Robertson-Walker (GRW) spacetimes whose ber has a parabolic universal Riemannian covering are proved under boundedness assumptions on the mean curvature function and suitable geometric assumptions

Downloads

Download data is not yet available.

References

L. J. Alas, A. Romero, M. Sanchez, Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes. Gen. Relativity Gravitation 27 (1995), 71-84. https://doi.org/10.1007/BF02105675 [2] M. Medina, J. A. S. Pelegran, Stochastically complete constant mean curvature spacelike hypersurfaces in generalized Robertson-Walker spacetimes. J. Geom. Phys. 214 (2025), Paper No. 105522, 10 pp. https://doi.org/10.1016/j.geomphys.2025.105522 [3] M. Medina, J. A. S. Pelegran, Rigidity results for stochastically complete maximal hypersurfaces in Generalized Robertson-Walker spacetimes. Lett. Math. Phys. 116 (2026), no. 2, Paper No. 29, 17 pp. https://doi.org/10.1007/s11005-026-02064-w [4] B. ONeill, Semi-Riemannian geometry with applications to relativity, Academic Press, Inc., Harcourt Brace Jovanovich, Publishers, New York, (1983). https://doi.org/10.1090/S0273-0979-1987-15529-7 [5] J. A. S. Pelegran, A. Romero, R. M. Rubio, Uniqueness of complete maximal hypersurfaces in spatially open (n+1)-dimensional Robertson-Walker spacetimes with at ber. Gen. Relativity Gravitation 48 (2016), no. 6, 48-70. https://doi.org/10.1007/s10714-016-2069-7 [6] A. Romero, R. M. Rubio, J. J. Salamanca, Uniqueness of complete maximal hypersurfaces in spatially parabolic generalized Robertson-Walker spacetimes. Classical Quantum Gravity 30 (2013), 115007. pp. 13. https://doi.org/10.1088/0264-9381/30/11/115007 [7] A. Romero, R. M. Rubio, J. J. Salamanca, A new approach for uniqueness of complete maximal hypersurfaces in spatially parabolic GRW spacetimes. J. Math. Anal. Appl. 419 (2014), 355-372. https://doi.org/10.1016/j.jmaa.2014.04.063

F. Roing, E. A. Jr. Lima, Rigidity of parabolic and stable spacelike hypersurfaces in a generalized Robertson-Walker spacetime. J. Geom. 111 (2020), no. 2, Paper No. 30, 19 pp. https://doi.org/10.1007/s00022-020-00540-9 [9] N. Zhang, Z. Zhu, On Calabi-Bernsteins problem for uniqueness of complete spacelike hypersurfaces in weighted generalized Robertson-Walker spacetimes. Mathematics (2023), 11, 2795. https://doi.org/10.3390math11132795 [10] N. Zhang, A rigidity theorem on spacelike hypersurfaces in generalized Robertson-Walker spacetimes. Axioms (2026), 15, 241. https://doi.org/10.3390/axioms15030241

Downloads

Published

2026-05-15

How to Cite

Zhang, N. (2026). On the mean curvature of spacelike hypersurfaces in spatially parabolic GRW spacetimes. JOURNAL OF ADVANCES IN MATHEMATICS, 25, 40–44. https://doi.org/10.24297/jam.v25i.9897

Issue

Section

Articles