Zhiyuan Geng

activity

20242026

collaborators

4 papers

math.AP2026

Classification of minimizing solutions to a two-dimensional Allen-Cahn system

Zhiyuan Geng

We study bounded entire solutions $u : R^{2} \to R^{2}$ that minimize the Allen-Cahn functional \begin{equation*} J(u,Ω)=\int_Ω\left(\frac12 |\nabla u|^2+W(u)\right)\,d\…

math.AP2025

Half-space minimizing solutions of a two dimensional Allen-Cahn system

Zhiyuan Geng

This paper studies minimizing solutions to a two dimensional Allen-Cahn system on the upper half plane, subject to Dirichlet boundary conditions, \begin{equation*} Δu-\nabla_u W(u)…

math.AP2024

Rigidity results for a triple junction solution of Allen-Cahn system

Zhiyuan Geng

For the two dimensional Allen-Cahn system with a triple-well potential, previous results established the existence of a minimizing solution $u : R^{2} \to R^{2}$ …

math.AP2024

Uniqueness of the blow-down limit for triple junction problem

Zhiyuan Geng

We prove the uniqueness of $L^{1}$ blow-down limit at infinity for an entire minimizing solution $u : R^{2} \to R^{2}$ of a planar Allen-Cahn system with a triple-w…