Remark on isolated removable singularities of harmonic maps in two dimensions

For a ball \(B_R(0)\subset\mathbb{R}^2\), we provide sufficient conditions such that a harmonic map \(u\in C^\infty(B_R(0)\setminus\{0\}, N)\), with a self-similar bound on its gradient, belong to \(C^\infty(B_R(0))\). These conditions also guarantee the triviality of such harmonic maps when \(R=\infty\). For more information see https://ejde.math.txstate.edu/Volumes/2025/85/abstr.html