Integral inequalities for maximal spacelike hypersurfaces in the indefinite space form (Q1295485)

The author gives two integral inequalities for \(n\)-dimensional compact maximal spacelike hypersurfaces in an \((n+1)\)-dimensional indefinite space form \(N_1^{n+1}(c)\). We note that the following result is well-known: any \(n\)-dimensional complete maximal spacelike hypersurface in an \((n+1)\)-dimensional indefinite space form \(N_1^{n+1}(c)\) \((c\geq 0)\) is totally geodesic [see \textit{S. Y. Cheng} and \textit{S.-T. Yau}, Ann. Math. 104, 407-419 (1976; Zbl 0352.53021); also see reviewer's generalization: Soochow J. Math. 23, 79-89 (1997; Zbl 0870.53048)]. We also know that ``complete'' implies ``compact''. Therefore, the results of the paper under review only make sense when \(c<0\). For the results of complete maximal spacelike hypersurfaces in \(N_1^{n+1}(c)\) \((c<0)\), readers can consult \textit{T. Ishihara}'s paper [Mich. Math. J. 35, 345-352 (1988; Zbl 0682.53055)] and the above reviewer's paper.