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

Abstract

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.