Linear distortion and rescaling for quasiregular values
| Autor: | Kangasniemi, Ilmari, Onninen, Jani |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Sobolev mappings exhibiting only pointwise quasiregularity-type bounds have arisen in various applications, leading to a recently developed theory of quasiregular values. In this article, we show that by using rescaling, one obtains a direct bridge between this theory and the classical theory of quasiregular maps. More precisely, we prove that a non-constant mapping $f \colon \Omega \to \mathbb{R}^n$ with a $(K, \Sigma)$-quasiregular value at $f(x_0)$ can be rescaled at $x_0$ to a non-constant $K$-quasiregular mapping. Our proof of this fact involves establishing a quasiregular values -version of the linear distortion bound of quasiregular mappings. A quasiregular values variant of the small $K$ -theorem is obtained as an immediate corollary of our main result. Comment: 29 pages, 3 figures. v2 fixes a color rendering issue in the included TikZ-generated figures, and makes several technical changes to fix issues in the HTML version |
| Databáze: | arXiv |
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