Small data scattering for energy-subcritical and critical Nonlinear   Klein Gordon equations on product spaces
  We study small data scattering of solutions to Nonlinear Klein-Gordon equations with suitable pure power nonlinearities, posed on $\mathbb{R}^d\times \mathcal{M}^k$ with $k\leq2$ and $d\geq1$ and $\mathcal{M}^k$ a compact Riemannian manifold. As a special case we cover the $H^1-$critical NLKG on $\mathbb{R} \times M^2$. 
Lysianne Hari and Nicola Visciglia
math.AP math-ph math.MP