Sharp eigenvalue estimates of closed H -hypersurfaces in locally symmetric spaces

Eudes L. de Lima; Henrique F. de Lima; Fábio R. dos Santos; Marco A. L. Velásquez

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 969-981
  • ISSN: 0011-4642

Abstract

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The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.

How to cite

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de Lima, Eudes L., et al. "Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces." Czechoslovak Mathematical Journal 69.4 (2019): 969-981. <http://eudml.org/doc/294481>.

@article{deLima2019,
abstract = {The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.},
author = {de Lima, Eudes L., de Lima, Henrique F., dos Santos, Fábio R., Velásquez, Marco A. L.},
journal = {Czechoslovak Mathematical Journal},
keywords = {locally symmetric Riemannian space; closed $H$-hypersurface; strong stability; first stability eigenvalue},
language = {eng},
number = {4},
pages = {969-981},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces},
url = {http://eudml.org/doc/294481},
volume = {69},
year = {2019},
}

TY - JOUR
AU - de Lima, Eudes L.
AU - de Lima, Henrique F.
AU - dos Santos, Fábio R.
AU - Velásquez, Marco A. L.
TI - Sharp eigenvalue estimates of closed $H$-hypersurfaces in locally symmetric spaces
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 969
EP - 981
AB - The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.
LA - eng
KW - locally symmetric Riemannian space; closed $H$-hypersurface; strong stability; first stability eigenvalue
UR - http://eudml.org/doc/294481
ER -

References

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  1. Alencar, H., Carmo, M. P. do, 10.2307/2160241, Proc. Am. Math. Soc. 120 (1994), 1223-1229. (1994) Zbl0802.53017MR1172943DOI10.2307/2160241
  2. Alías, L. J., Barros, A., Jr., A. Brasil, 10.1090/S0002-9939-04-07559-8, Proc. Am. Math. Soc. 133 (2005), 875-884. (2005) Zbl1065.53046MR2113939DOI10.1090/S0002-9939-04-07559-8
  3. Alías, L. J., Jr., A. Brasil, Perdomo, O., 10.1090/S0002-9939-07-08886-7, Proc. Am. Math. Soc. 135 (2007), 3685-3693. (2007) Zbl1157.53030MR2336585DOI10.1090/S0002-9939-07-08886-7
  4. Alías, L. J., Lima, H. F. de, Meléndez, J., Santos, F. R. dos, 10.1002/mana.201400296, Math. Nachr. 289 (2016), 1309-1324. (2016) Zbl1350.53078MR3541811DOI10.1002/mana.201400296
  5. Alías, L. J., Kurose, T., Solanes, G., 10.1016/j.difgeo.2006.02.008, Differ. Geom. Appl. 24 (2006), 492-502. (2006) Zbl1103.52006MR2254052DOI10.1016/j.difgeo.2006.02.008
  6. Alías, L. J., Meroño, M. A., Ortiz, I., 10.1007/s00009-014-0397-y, Mediterr. J. Math. 12 (2015), 147-158. (2015) Zbl1316.53062MR3306032DOI10.1007/s00009-014-0397-y
  7. Barros, A. A. de, Jr., A. C. Brasil, Jr., L. A. M. de Sousa, 10.2996/kmj/1085143788, Kodai Math. J. 27 (2004), 45-56. (2004) Zbl1059.53047MR2042790DOI10.2996/kmj/1085143788
  8. Gomes, J. N., Lima, H. F. de, Santos, F. R. dos, Velásquez, M. A. L., 10.1016/j.na.2015.11.026, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 133 (2016), 15-27. (2016) Zbl1333.53090MR3449745DOI10.1016/j.na.2015.11.026
  9. Melendéz, J., 10.1007/s00574-014-0055-9, Bull. Braz. Math. Soc. 45 (2014), 385-404. (2014) Zbl1319.53065MR3264798DOI10.1007/s00574-014-0055-9
  10. Meroño, M. A., Ortiz, I., 10.1016/j.jmaa.2015.10.016, J. Math. Anal. Appl. 434 (2016), 1779-1788. (2016) Zbl1328.53075MR3415751DOI10.1016/j.jmaa.2015.10.016
  11. Meroño, M. A., Ortiz, I., 10.1016/j.difgeo.2015.11.009, Differ. Geom. Appl. 45 (2016), 67-77. (2016) Zbl1334.53061MR3457388DOI10.1016/j.difgeo.2015.11.009
  12. Okumura, M., 10.2307/2373587, Am. J. Math. 96 (1974), 207-213. (1974) Zbl0302.53028MR0353216DOI10.2307/2373587
  13. Perdomo,, O., 10.1090/S0002-9939-02-06451-1, Proc. Am. Math. Soc. 130 (2002), 3379-3384. (2002) Zbl1014.53036MR1913017DOI10.1090/S0002-9939-02-06451-1
  14. Simons, J., 10.2307/1970556, Ann. Math. 88 (1968), 62-105. (1968) Zbl0181.49702MR0233295DOI10.2307/1970556
  15. Velásquez, M. A. L., Lima, H. F. de, Santos, F. R. dos, Aquino, C. P., 10.2989/16073606.2017.1305463, Quaest. Math. 40 (2017), 605-616. (2017) MR3691472DOI10.2989/16073606.2017.1305463
  16. Wu, C., 10.1007/BF01198725, Arch. Math. 61 (1993), 277-284. (1993) Zbl0791.53056MR1231163DOI10.1007/BF01198725

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