The Liouville theorem of homeomorphism with integrable dilatation (Q2735429)
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scientific article; zbMATH DE number 1640430
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Liouville theorem of homeomorphism with integrable dilatation |
scientific article; zbMATH DE number 1640430 |
Statements
30 August 2001
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quasiconformal mapping
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Liouville theorem
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The Liouville theorem of homeomorphism with integrable dilatation (English)
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The Liouville theorem for homeomorphisms of \(\mathbb{R}^n\) with integrable dilatations is shown, under the following condition: NEWLINE\[NEWLINE\int_{\mathbb{R}^n \setminus B^n(r)} {H^{n-1}(x,f) \over|x|^n} dm<+\infty,NEWLINE\]NEWLINE where \(H(x,f)\) is the local dilatation of \(f\) at \(x\).
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