  We study global dynamics for the focusing nonlinear Klein-Gordon equation
with the energy-critical nonlinearity in two or higher dimensions when the
energy equals the threshold given by the ground state of a mass-shifted
equation, and prove that the solutions are divided into scattering and blowup.
In short, the Kenig-Merle scattering/blowup dichotomy extends to the threshold
energy in the case of mass-shift for the critical nonlinear Klein-Gordon
equation.
