On estimation of the Dirichlet spectral gap (Q5927598)

The aim of the paper is to study the lower bound estimate of \(\lambda_2-\lambda_1\), where \(\lambda_1\), \(\lambda_2\) are the first two Dirichlet eigenvalues of the Laplacian of \(\overline{\Omega}\), \(\Omega\subset M\), \(M\) is a complete Riemannian manifold of dimension \(d\), and \(\Omega\) a convex regular open domain with diameter \(D\). Using a general lower bound formula of the spectral gap given by \textit{M. F. Chen} and \textit{F. Y. Wang} [Sci. China, Ser. A 40, No. 4, 384-394 (1997; Zbl 0895.58056)] a lower bound for the case of constant curvature is given.