A note on maximal spacelike hypersurfaces in a generalized Robertson-Walker spacetime
Commun. Korean Math. Soc.
Published online December 28, 2021
Henrique de Lima
Federal University of Campina Grande
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 spacelike 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 spacelike hypersurfaces; entire graphs; maximal spacelike hypersurface equation.
MSC numbers : Primary: 53C42; Secondary: 53C50.
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