Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2022; 37(3): 893-904

Online first article December 28, 2021      Printed July 31, 2022

https://doi.org/10.4134/CKMS.c210233

Copyright © The Korean Mathematical Society.

A note on maximal hypersurfaces in a generalized Robertson-Walker spacetime

Henrique Fernandes de~Lima

Universidade Federal de Campina Grande

Abstract

In this note, we apply a maximum principle related to vo-lu-me growth of a complete noncompact Riemannian manifold, which was recently obtained by Al'{i}as, Caminha and do Nascimento in~cite{Alias-Caminha-Nascimento}, to es-ta-blish 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

MSC numbers: Primary 53C42; Secondary 53C50

Stats or Metrics

Share this article on :

Related articles in CKMS