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

• Autorzy: Antonio W. Cunha , Eudes L. de Lima , Henrique F. de Lima , Eraldo A. Lima Jr. , Adriano A. Medeiros
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53B30: Lorentz metrics, indefinite metrics
• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 53C50: Lorentz manifolds, manifolds with indefinite metrics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 233
• Numer: 2
• Strony: 183-196

Daty

wydano

2016

Twórcy

autor

Antonio W. Cunha

• Departamento de Matemática, Universidade Federal do Piauí, 64049-550 Teresina, Piauí, Brazil

autor

Eudes L. de Lima

• Campus Pau dos Ferros, Universidade Federal Rural do Semi-Árido, 59900-000 Pau dos Ferros, Rio Grande do Norte, Brazil

autor

Henrique F. de Lima

• Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil

autor

Eraldo A. Lima Jr.

• Departamento de Matemática, Universidade Federal da Paraíba, 58051-900 João Pessoa, Paraíba, Brazil

autor

Adriano A. Medeiros

• Departamento de Matemática, Universidade Federal da Paraíba, 58051-900 João Pessoa, Paraíba, Brazil

Identyfikatory

DOI

10.4064/sm8464-4-2016