Description |
We shall talk about eigenvalues of the Laplace operator on hyperbolic surfaces. The main focus of the talk would be on 'small eigenvalues' i.e. eigenvalues in the interval (0, 1/4]. We shall recall a method, due to P. Buser, to show that surfaces with small eigenvalues do exist. If time permits, we shall discuss the result of Otal-Rosas on upper bound on the number of such eigenvalues depending on the topology of the surface. |