Global solutions for nonlinear Klein–Gordon equations in infinite homogeneous waveguides

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