Some lifting and approximation properties for maps in $W^{1,2}(\mathbb{B}^3;\mathbb{S}^2)$
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| Format: | Preprint |
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2026
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| _version_ | 1866913127349616640 |
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| author | Guerra, André Lamy, Xavier Zemas, Konstantinos |
| author_facet | Guerra, André Lamy, Xavier Zemas, Konstantinos |
| contents | Smooth maps $u\colon\mathbb B^3\to\mathbb S^2$ can be lifted to $\hat u\colon\mathbb B^3\to\mathbb S^3$ using the Hopf fibration $h\colon \mathbb S^3\to\mathbb S^2$ via the factorization $u=h\circ\hat u$. In this note we characterize the $W^{1,2}$-maps which have this lifting property in terms of exactness of the pullback form $u^*ω_{\mathbb S^2}$, and deduce a smooth approximation property preserving the constraint $u^*ω_{\mathbb S^2}=dη$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_14507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some lifting and approximation properties for maps in $W^{1,2}(\mathbb{B}^3;\mathbb{S}^2)$ Guerra, André Lamy, Xavier Zemas, Konstantinos Analysis of PDEs 26D10, 30C70, 49Q20 Smooth maps $u\colon\mathbb B^3\to\mathbb S^2$ can be lifted to $\hat u\colon\mathbb B^3\to\mathbb S^3$ using the Hopf fibration $h\colon \mathbb S^3\to\mathbb S^2$ via the factorization $u=h\circ\hat u$. In this note we characterize the $W^{1,2}$-maps which have this lifting property in terms of exactness of the pullback form $u^*ω_{\mathbb S^2}$, and deduce a smooth approximation property preserving the constraint $u^*ω_{\mathbb S^2}=dη$. |
| title | Some lifting and approximation properties for maps in $W^{1,2}(\mathbb{B}^3;\mathbb{S}^2)$ |
| topic | Analysis of PDEs 26D10, 30C70, 49Q20 |
| url | https://arxiv.org/abs/2605.14507 |