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Analysis provides criteria for harmonic maps' continuity and triviality in two dimensions, indicating limits of singular behavior.
For a ball \(B_R(0)^2\), we provide sufficient conditions such that a harmonic map \(u∈ C^∞(B_R(0)\{0\}, N)\), with a self-similar bound on its gradient, belong to \(C^∞(B_R(0))\). These conditions also guarantee the triviality of such harmonic maps when \(R=∞\). For more information see https://ejde.math.txstate.edu/Volumes/2025/85/abstr.html
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Changyou Wang (2025) studied this question.
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