Author

Jun-Cheng Wei

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Preprint Oct 2026

Sheeting property and rigidity for stable solutions to the Allen--Cahn equation

We prove a sheeting theorem for stable solutions to the Allen--Cahn equation in ambient dimensions $2$ through $10$. We show that weak convergence of the measures $\varepsilon|Du_\varepsilon|^2\,dX$ to a hyperplane with integer multiplicity implies that the zero sets are disjoint smooth graphs. As a consequence, stable...

Yong Liu, Tian-Ci Luo, Ke-Lei Wang et al. · 0 citations

Preprint Sep 2026

Stable De Giorgi conjecture of the Allen--Cahn equation in $\mathbb{R}^3$

We prove that every bounded stable entire solution $v$ of the Allen--Cahn equation in $\R^3$ is one-dimensional. As a consequence, the full De Giorgi conjecture in $\mathbb{R}^4$ is true. We also obtain local curvature estimates for stable solutions. The proof strategy is inspired by the recent breakthrough work of Cha...

Yong Liu, Tian-Ci Luo, Ke-Lei Wang et al. · 0 citations