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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2511.19357 |
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| _version_ | 1866918303427985408 |
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| author | Soultanis, Elefterios |
| author_facet | Soultanis, Elefterios |
| contents | We use Almgren's framework of multi-valued maps to construct a multi-valued inverse $F:f(Ω)\to \mathcal A_d(\mathbb R^n)$ of a quasiregular map $f:Ω\to \mathbb R^n$ of finite degree $d$. We then develop a pull-back theory of differential forms on $\mathcal A_d(\mathbb R^n)$ by Sobolev maps, and use it to show that the multi-valued inverse is a quasiregular $ω$-curve (in the sense of Pankka) with respect to a natural $n$-form $ω$ (suitably interpreted). The pull-back theory is of independent interest, and allows us to conclude e.g. higher Sobolev integrability and quasiminimality of the multi-valued inverse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pull-back of differential forms by multi-valued Sobolev maps, and the quasiregularity of the multi-valued inverse of a quasiregular map Soultanis, Elefterios Differential Geometry Complex Variables 30C65, 35R70, 53C23, 30L10 We use Almgren's framework of multi-valued maps to construct a multi-valued inverse $F:f(Ω)\to \mathcal A_d(\mathbb R^n)$ of a quasiregular map $f:Ω\to \mathbb R^n$ of finite degree $d$. We then develop a pull-back theory of differential forms on $\mathcal A_d(\mathbb R^n)$ by Sobolev maps, and use it to show that the multi-valued inverse is a quasiregular $ω$-curve (in the sense of Pankka) with respect to a natural $n$-form $ω$ (suitably interpreted). The pull-back theory is of independent interest, and allows us to conclude e.g. higher Sobolev integrability and quasiminimality of the multi-valued inverse. |
| title | Pull-back of differential forms by multi-valued Sobolev maps, and the quasiregularity of the multi-valued inverse of a quasiregular map |
| topic | Differential Geometry Complex Variables 30C65, 35R70, 53C23, 30L10 |
| url | https://arxiv.org/abs/2511.19357 |