A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form

Henrique Fernandes de Lima

Address: Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraíba, Brazil

Abstract: We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].

AMSclassification: primary 53C42; secondary 53C50.

Keywords: Lorentzian space forms, complete spacelike hypersurfaces, polynomial volume growth, support functions.

DOI: 10.5817/AM2022-3-169