Small eigenvalues on Y-pieces and on Riemann surfaces (Q1173779)

The study of eigenvalues of the Laplacian of a compact Riemann surface with the hyperbolic metric is one of the most interesting topics in eigenvalue theory of compact surfaces. P. Buser proved, among other things, that a closed Riemann surface of genus \(g\) has at most \(4g-2\) eigenvalues smaller than 1/4. The author improves the above result showing that the bound \(4g-2\) can be changed by the sharper one \(4g-4\).