Geodesic
Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
Antonio W. Cunha 1   ; Eudes L. de Lima 2   ; Henrique F. de Lima 3   ; Eraldo A. Lima Jr. 4   ; Adriano A. Medeiros 4
1 Departamento de Matemática Universidade Federal do Piauí 64049-550 Teresina, Piauí, Brazil
2 Campus Pau dos Ferros Universidade Federal Rural do Semi-Árido 59900-000 Pau dos Ferros Rio Grande do Norte, Brazil
3 Departamento de Matemática Universidade Federal de Campina Grande 58429-970 Campina Grande, Paraíba, Brazil
4 Departamento de Matemática Universidade Federal da Paraíba 58051-900 João Pessoa, Paraíba, Brazil
Studia Mathematica, Tome 233 (2016) no. 2, pp. 183-196 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product $M^n\times _\rho \mathbb R$, whose curvature of the base $M^n$ satisfies certain constraints and whose warping function $\rho $ is concave on $M^n$. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, $L^1$-Liouville. Rigidity results related to entire Killing graphs constructed over the base of the ambient space are also given.
DOI : 10.4064/sm8464-4-2016
Keywords: purpose apply suitable maximum principles order obtain bernstein type properties two sided hypersurfaces immersed constant mean curvature killing warped product times rho mathbb whose curvature base satisfies certain constraints whose warping function rho concave study situations which these hypersurfaces supposed either parabolic stochastically complete general setting liouville rigidity results related entire killing graphs constructed base ambient space given

Antonio W. Cunha  1   ; Eudes L. de Lima  2   ; Henrique F. de Lima  3   ; Eraldo A. Lima Jr.  4   ; Adriano A. Medeiros  4

1 Departamento de Matemática Universidade Federal do Piauí 64049-550 Teresina, Piauí, Brazil
2 Campus Pau dos Ferros Universidade Federal Rural do Semi-Árido 59900-000 Pau dos Ferros Rio Grande do Norte, Brazil
3 Departamento de Matemática Universidade Federal de Campina Grande 58429-970 Campina Grande, Paraíba, Brazil
4 Departamento de Matemática Universidade Federal da Paraíba 58051-900 João Pessoa, Paraíba, Brazil 
@article{10_4064_sm8464_4_2016,
     author = {Antonio W. Cunha and Eudes L. de Lima and Henrique F. de Lima and Eraldo A. Lima Jr. and Adriano A. Medeiros},
     title = {Bernstein type properties of two-sided hypersurfaces immersed in a {Killing} warped product},
     journal = {Studia Mathematica},
     pages = {183--196},
     year = {2016},
     volume = {233},
     number = {2},
     doi = {10.4064/sm8464-4-2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8464-4-2016/}
}
TY  - JOUR
AU  - Antonio W. Cunha
AU  - Eudes L. de Lima
AU  - Henrique F. de Lima
AU  - Eraldo A. Lima Jr.
AU  - Adriano A. Medeiros
TI  - Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
JO  - Studia Mathematica
PY  - 2016
SP  - 183
EP  - 196
VL  - 233
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm8464-4-2016/
DO  - 10.4064/sm8464-4-2016
LA  - en
ID  - 10_4064_sm8464_4_2016
ER  - 
%0 Journal Article
%A Antonio W. Cunha
%A Eudes L. de Lima
%A Henrique F. de Lima
%A Eraldo A. Lima Jr.
%A Adriano A. Medeiros
%T Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
%J Studia Mathematica
%D 2016
%P 183-196
%V 233
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm8464-4-2016/
%R 10.4064/sm8464-4-2016
%G en
%F 10_4064_sm8464_4_2016
Antonio W. Cunha; Eudes L. de Lima; Henrique F. de Lima; Eraldo A. Lima Jr.; Adriano A. Medeiros. Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product. Studia Mathematica, Tome 233 (2016) no. 2, pp. 183-196. doi: 10.4064/sm8464-4-2016

Cité par Sources :