August 17, 2025Open Access

Remark on isolated removable singularities of harmonic maps in two dimensions

Key Points

Harmonic maps can exhibit triviality when R approaches infinity, ensuring smooth behavior across domains.
Conditions are outlined to establish that harmonic maps belong to C^∞ in neighborhoods devoid of isolated singularities.
Analysis focuses on maps in R^2, emphasizing the role of self-similar bounds on gradients for characterizing singular behavior.
Significance lies in offering a formal approach to understanding isolated singularities of harmonic maps in higher dimensions.

Abstract

For a ball \ (BR (0) ²\), we provide sufficient conditions such that a harmonic map \ (u C^ (BR (0) \0\, N) \), with a self-similar bound on its gradient, belong to \ (C^ (BR (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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Cite This Study

Changyou Wang (Mon,) studied this question.

synapsesocial.com/papers/68a36de60a429f7973331511 https://doi.org/https://doi.org/10.58997/ejde.2025.85

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