Heinz-Schwarz inequalities for harmonic mappings in the unit ball (Q2790833)
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scientific article; zbMATH DE number 6551801
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Heinz-Schwarz inequalities for harmonic mappings in the unit ball |
scientific article; zbMATH DE number 6551801 |
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Heinz-Schwarz inequalities for harmonic mappings in the unit ball (English)
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8 March 2016
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harmonic mappings
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Heinz inequality
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Schwarz inequality
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0.92565084
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0.9132242
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0.9100194
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0.90599996
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The first main result obtained by the author is a generalization of the harmonic Schwarz lemma to the unit ball \(B\) in \(\mathbb R^d\) with \(d\geq 3\). For \(d=2\) the result is known.NEWLINENEWLINEThe second one concerns the Heinz inequality on the boundary of the unit ball and gives a sharp constant \(C_n\) in the inequality NEWLINE\[NEWLINE\|\partial_ru(r\eta)\|_{r=1}\geq C_n,\quad \|\eta\|=1,NEWLINE\]NEWLINENEWLINEfor every proper harmonic map \(u\) from \(B\) onto \( B\) such that \(u(0)=0\).
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