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http://dx.doi.org/10.4134/CKMS.c210233

A NOTE ON MAXIMAL HYPERSURFACES IN A GENERALIZED ROBERTSON-WALKER SPACETIME  

de Lima, Henrique Fernandes (Departamento de Matematica Universidade Federal de Campina Grande)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 893-904 More about this Journal
Abstract
In this note, we apply a maximum principle related to volume growth of a complete noncompact Riemannian manifold, which was recently obtained by Alías, Caminha and do Nascimento in [4], to establish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.
Keywords
Generalized Robertson-Walker spacetimes; timelike convergence condition; maximal hypersurfaces; entire graphs; maximal hypersurface equation;
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