Co-dimension one stable blowup for the supercritical cubic wave equation

For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution u^∗_T , which is defined on the whole space and exists in all supercritical dimensions d ≥ 5. For d = 7, we analyze its stability properties without any symmetry assumptions and prove the existence of a co-dimension one Lipschitz manifold consisting of initial data whose solutions blowup in finite time and converge asymptotically to u^∗_T (modulo space-time shifts and Lorentz boosts) in the backward lightcone of the blowup point. The underlying topology is strictly above scaling.