Let be a closed embedded minimal hypersurface in the unit sphere S^m+1 and let =_|A| be the norm of its second fundamental form. In this work, we prove that the first eigenvalue of the Laplacian of satisfies ₁ () > m2+m (m+1) 32 (12 +m+11) ^{2+8}, and ₁ () =m when. In particular, this estimate improves the one obtained recently in Duncan–Sire–Spruck (2024). The proof of our main result is based on a Rayleigh quotient estimate for a harmonic extension of an eigenfunction of the Laplacian of in the spirit of Choi and Wang (1983).
Jiménez et al. (Mon,) studied this question.