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Abstract
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It is well-known that some minimal (or maximal) hypersurfaces are stable. However, there is a growing recognition on unstable minimal (or maximal) hypersurfaces by introducing the concept of index of stability. Firstly, the index of stability for minimal hypersurfaces in the Euclidean n-sphere has been introduced by J. Simons [20], which is followed
recently by many people (see for instance [3, 9, 18, 21]). Also, Barros and Sousa in [10] have
payed attention to the concept of index of r-stability (as the r-extension of index of stability)
on r-minimal hypersurfaces in the Euclidean n-sphere. Thy gave low bounds for r-stability
index ofr-minimal n-dimensional closed hypersurfaces in S n +1. In this paper we give low
bounds for the r-stability index ofr-maximal closed spacelike hypersurfaces in the de Sitter
space S1n +1
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