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 , 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.