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=\i...
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| Published in | Electronic journal of differential equations Vol. 2025; no. 1-??; pp. 85 - 5 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Texas State University
11.08.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1072-6691 1072-6691 |
| DOI | 10.58997/ejde.2025.85 |
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| Abstract | 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 |
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| AbstractList | 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 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 $R=\infty$. |
| Author | Wang, Changyou |
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| Snippet | 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... 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... |
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| Title | Remark on isolated removable singularities of harmonic maps in two dimensions |
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