A first eigenvalue estimate for embedded hypersurfaces in positive Ricci curvature manifolds

Let $Σ$ be a closed, embedded, oriented hypersurface in a closed oriented Riemannian manifold $N$. Under a lower bound on the Ricci curvature and an upper bound on the sectional curvature of $N$, we establish a lower bound for the first nonzero eigenvalue of the Laplacian on $Σ$. The estimate depends on the ambient curvature bounds, the normal injectivity radius, and the geometry of $Σ$ through its mean curvature and second fundamental form. This result extends the classical eigenvalue estimate of Choi and Wang [J. Diff. Geom. \textbf{18} (1983), 559--562.] to the non-minimal case.

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