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. © 2006 Elsevier Inc. All rights reserved.