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 x 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. (c) 2006 Elsevier Inc. All rights reserved.