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<p>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.</p>

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Optimal estimates for the first eigenvalue of a class of Schrödinger operators associated to a spacelike hypersurface in Einstein spacetimes

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  • 发表日期：

    2026年4月29日

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  • Henrique F. de Lima,
  • Ary V. F. Leite,
  • Marco A. L. Velásquez

摘要

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.