On De Giorgi Conjecture in Dimension $N\ge 9$

Manuel del Pino, Mike Kowalczyk, Juncheng Wei

A celebrated conjecture due to De Giorgi states that any bounded solution of the equation $\Delta u+(1-u^2)u=0in{\mathbb{R}}^N$ with $\pp_{y_N}u >0$ must be such that its level sets…