Global existence for nonlinear Klein–Gordon equations in infinite homogeneous waveguides in two dimensions

In this paper we prove a global existence result for nonlinear Klein–Gordon equations with small data in infinite homogeneous waveguids, R2×M, where M=(M,g) is a Zoll manifold. The method is based on the normal forms, the eigenfunction expansion for M and the special distribution of eigenvalues of Laplace–Beltrami on Zoll manifold.