Global uniqueness theorems for linear and nonlinear waves

Understand

We prove a unique continuation from infinity theorem for regular waves of the form $[ \Box + \mathcal{V} (t, x) ]\phi=0$.

• Under the assumption of no incoming and no outgoing radiation on specific halves of past and future null infinities, we show that the solution must vanish everywhere.
• The "no radiation" assumption is captured in a specific, finite rate of decay which in general depends on the $L^\infty$-profile of the potential $\mathcal{V}$.
• We show that the result is optimal in many regards.