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This work derives optimal eigenvalue estimates of Schrödinger operators in spacelike hypersurfaces, indicating uniqueness outcomes for certain curvature conditions.
In this work, our aim is to obtain optimal estimates for the first eigenvalue of a class of Schrödinger operators associated to the mean curvature and the norm of the traceless second fundamental form of compact spacelike hypersurfaces immersed in an Einstein spacetime satisfying suitable curvature conditions. As application, we derive uniqueness results for spacelike hypersurfaces, whether they are totally umbilical or have two constant principal curvatures in these ambient spaces.
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Lima et al. (2026) studied this question.
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