Codimension One Threshold Manifold for the Critical gKdV Equation

We construct the "threshold manifold" near the soliton for the mass critical gKdV equation, completing results obtained in Martel et al. (Acta Math 212:59-140, 2014, J Math Eur Soc 2015). In a neighborhood of the soliton, this C (1) manifold of codimension one separates solutions blowing up in finite time and solutions in the "exit regime". On the manifold, solutions are global in time and converge locally to a soliton. In particular, the soliton behavior is strongly unstable by blowup.