2 citations · 2 across the 6 of their papers we have counts for
7 papers
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…
Global Convergence of the Gursky-Malchiodi -curvature Flow
Liuwei Gong, Sanghoon Lee, Juncheng Wei
In their seminal work, Gursky and Malchiodi introduced a non-local conformal flow in dimensions to resolve the constant -curvature problem. They proved sequential con…
Structural constraints on mobility edges in one-dimensional quasiperiodic systems
Sanghoon Lee, Tilen Cadez, Kyoung-Min Kim
Mobility edges commonly arise in one-dimensional quasiperiodic systems once exact self-duality is broken, yet their origin is typically understood only at the level of individual H…
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…
Rigidity of Poincaré-Einstein manifolds with flat Euclidean conformal infinity
Sanghoon Lee, Fang Wang
In this paper, we prove a rigidity theorem for Poincaré-Einstein manifolds whose conformal infinity is a flat Euclidean space. The proof relies on analyzing the propagation of curv…
Type-I Blowup Solutions for Yang-Mills Flow
Jaehwan Kim, Sanghoon Lee
In this paper, we construct an infinite-dimensional family of solutions for the Yang-Mills flow on for , which converge to -equi…
Quantum Phase Transitions and Dynamics in Perturbed Flatbands
Sanghoon Lee
In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme…