Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
Studia Mathematica, Tome 233 (2016) no. 2, pp. 183-196
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Antonio W. Cunha 1 ; Eudes L. de Lima 2 ; Henrique F. de Lima 3 ; Eraldo A. Lima Jr. 4 ; Adriano A. Medeiros 4
@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},
publisher = {mathdoc},
volume = {233},
number = {2},
year = {2016},
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 PB - mathdoc 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 %I mathdoc %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
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