A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form

Henrique Fernandes de Lima

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 3, page 169-175
  • ISSN: 0044-8753

Abstract

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We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].

How to cite

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de Lima, Henrique Fernandes. "A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form." Archivum Mathematicum 058.3 (2022): 169-175. <http://eudml.org/doc/298350>.

@article{deLima2022,
abstract = {We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].},
author = {de Lima, Henrique Fernandes},
journal = {Archivum Mathematicum},
keywords = {Lorentzian space forms; complete spacelike hypersurfaces; polynomial volume growth; support functions},
language = {eng},
number = {3},
pages = {169-175},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form},
url = {http://eudml.org/doc/298350},
volume = {058},
year = {2022},
}

TY - JOUR
AU - de Lima, Henrique Fernandes
TI - A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 3
SP - 169
EP - 175
AB - We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].
LA - eng
KW - Lorentzian space forms; complete spacelike hypersurfaces; polynomial volume growth; support functions
UR - http://eudml.org/doc/298350
ER -

References

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  1. Alías, L.J., 10.3836/tjm/1255958315, Tokyo J. Math. 24 (2001), 107–112. (2001) MR1844421DOI10.3836/tjm/1255958315
  2. Alías, L.J., Brasil Jr., A., Perdomo, O., 10.1007/s12220-008-9029-8, J. Geom. Anal. 18 (2008), 687–703. (2008) MR2420759DOI10.1007/s12220-008-9029-8
  3. Alías, L.J., Caminha, A., do Nascimento, F.Y., A maximum principle related to volume growth and applications, Ann. Mat. Pura Appl. 200 (2021), 1637–1650. (2021) MR4278219
  4. Alías, L.J., Pastor, J.A., 10.1016/S0393-0440(98)00014-X, J. Geom. Phys. 28 (1998), 85–93. (1998) MR1653134DOI10.1016/S0393-0440(98)00014-X
  5. Aquino, C.P., de Lima, H.F., 10.1016/j.jmaa.2011.08.046, J. Math. Anal. Appl. 386 (2012), 862–869. (2012) MR2834793DOI10.1016/j.jmaa.2011.08.046
  6. Aquino, C.P., de Lima, H.F., 10.4171/CMH/329, Comment. Math. Helv. 89 (2014), 617–629. (2014) MR3260844DOI10.4171/CMH/329
  7. Aquino, C.P., de Lima, H.F., 10.1007/s00208-014-1049-z, Math. Ann. 360 (2014), 555–569. (2014) MR3273637DOI10.1007/s00208-014-1049-z
  8. Aquino, C.P., de Lima, H.F., dos Santos, F.R., On the quadric CMC spacelike hypersurfaces in Lorentzian space forms, Colloq. Math. 145 (2016), 89–98. (2016) MR3514262
  9. Aquino, C.P., de Lima, H.F., Velásquez, M.A.L., 10.1007/s10711-014-0002-3, Geom. Dedicata 174 (2015), 13–23. (2015) MR3303038DOI10.1007/s10711-014-0002-3
  10. Beem, J.K., Ehrlich, P.E., Easley, K.L., Global Lorentzian Geometry, CRC Press, New York, 1996, Second Edition. (1996) MR1384756
  11. Galloway, G.J., Senovilla, J.M.M., 10.1088/0264-9381/27/15/152002, Classical Quantum Gravity 27 (15) (2010), 10pp., 152002. (2010) MR2659235DOI10.1088/0264-9381/27/15/152002
  12. Hawking, S.W., Ellis, G.F.R., The large scale structure of spacetime, Cambridge University Press, London-New York, 1973. (1973) MR0424186
  13. Montiel, S., 10.1007/s002080050306, Math. Ann. 314 (1999), 529–553. (1999) MR1704548DOI10.1007/s002080050306
  14. O’Neill, B., Semi-Riemannian Geometry, with Applications to Relativity, Academic Press, New York, 1983. (1983) MR0719023
  15. Penrose, R., 10.1103/PhysRevLett.14.57, Phys. Rev. Lett. 14 (1965), 57–59. (1965) MR0172678DOI10.1103/PhysRevLett.14.57
  16. Senovilla, J.M.M., Singularity theorems in general relativity: Achievements and open questions, Einstein and the Changing Worldviews of Physics (Christoph Lehner, Jürgen Renn, Schemmel, Matthias, eds.), Birkhäuser Boston, 2012, pp. 305–316. (2012) 

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