Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product

Antonio W. Cunha, et al. "Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product." Studia Mathematica 233.2 (2016): 183-196. <http://eudml.org/doc/285827>.

@article{AntonioW2016,
abstract = {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 $Mⁿ ×_\{ρ\} ℝ$, whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related to entire Killing graphs constructed over the base of the ambient space are also given.},
author = {Antonio W. Cunha, Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Lima Jr., Adriano A. Medeiros},
journal = {Studia Mathematica},
keywords = {Killing warped product; parabolic hypersurfaces; stochastically complete hypersurfaces; L1-Liouville hypersurfaces; entire Killing graphs},
language = {eng},
number = {2},
pages = {183-196},
title = {Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product},
url = {http://eudml.org/doc/285827},
volume = {233},
year = {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
VL - 233
IS - 2
SP - 183
EP - 196
AB - 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 $Mⁿ ×_{ρ} ℝ$, whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related to entire Killing graphs constructed over the base of the ambient space are also given.
LA - eng
KW - Killing warped product; parabolic hypersurfaces; stochastically complete hypersurfaces; L1-Liouville hypersurfaces; entire Killing graphs
UR - http://eudml.org/doc/285827
ER -