Shrinking cone energy argument
= Shrinking cone energy argument
For the homogeneous speed-one <wave equation>, integrate its <wave energy> density over $B(x_*,T-t)$. The moving boundary contributes $-e$, while the usual flux contributes $u_t\partial_nu$. Their sum is $-\frac12(u_t-\partial_nu)^2-\frac12|\nabla_{\mathrm{tan}}u|^2\leq0$. Zero <Cauchy data> in the initial ball therefore force zero solution in its backward <light cone>.