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

Let $\mathrm{\Sigma }$ 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 $\mathrm{\Sigma }$. The estimate depends on the ambient curvature bounds, the normal injectivity radius, and the geometry of $\mathrm{\Sigma }$ through its mean curvature and second fundamental form. This result extends the classical eigenvalue estimate of Choi and Wang [J. Diff. Geom. $\mathbf{\text{18}}$ (1983), 559–562.] to the non-minimal case.