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20242026
most citedStructural constraints on mobility edges in one-dimensional quasiperiodic systems

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math.AP2026

A Half-Space Theorem for the Allen--Cahn Equation in All Dimensions

Sanghoon Lee

We prove that, in every dimension, a bounded, non-constant entire solution of the Allen--Cahn equation whose zero set is contained in a half-space is a one-dimensional heteroclinic…

math.AP2026

Nodal set comparison for Allen--Cahn solutions with conical asymptotics

Sanghoon Lee, Taehun Lee

We establish a comparison principle for entire solutions of the Allen--Cahn equation whose nodal sets, possibly singular, are asymptotic to a regular minimizing hypercone. We show…