Electron. J. Differential Equations, Vol. 2018 (2018), No. 80, pp. 1-14.

Solutions to the maximal spacelike hypersurface equation in generalized Robertson-Walker spacetimes

Henrique F. de Lima, Fabio R. dos Santos, Jogli G. Araujo

Abstract:
We apply some generalized maximum principles for establishing uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime, which is supposed to obey the so-called timelike convergence condition (TCC). As application, we study the uniqueness and nonexistence of entire solutions of a suitable maximal spacelike hypersurface equation in GRW spacetimes obeying the TCC.

Submitted August 12, 2017. Published March 20, 2018.
Math Subject Classifications: 53C42, 53B30, 53C50, 53Z05, 83C99.
Key Words: Generalized Robertson-Walker spacetimes; timelike convergence ; maximal spacelike hypersurfaces; entire graphs; maximal spacelike hypersurface equation.

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Henrique F. de Lima
Departamento de Matemática
Universidade Federal de Campina Grande
58429-970 Campina Grande, Paraíba, Brazil
email: henrique@mat.ufcg.edu.br
Fábio R. dos Santos
Departamento de Matemática
Universidade Federal de Campina Grande
58429-970 Campina Grande, Paraíba, Brazil
email: fabio@mat.ufcg.edu.br
Jogli G. Araújo
Departamento de Matemática
Universidade Federal de Campina Grande
58429-970 Campina Grande, Paraíba, Brazil
email: jogli@mat.ufcg.edu.br

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