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ON EXTREMALITY AND UNIQUE EXTREMALITY OF TEICHM\"ULLER MAPPINGS |
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Citation: |
Lai Wancai,Wu Zhemin.ON EXTREMALITY AND UNIQUE EXTREMALITY OF TEICHM\"ULLER MAPPINGS[J].Chinese Annals of Mathematics B,1995,16(3):399~406 |
Page view: 1077
Net amount: 725 |
Authors: |
Lai Wancai; Wu Zhemin |
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Abstract: |
Consider the Teichm\"uller mapping $f$ associated with $\vp$ in
the unit disc $D$ and the class of all quasiconformal mappings in
$D$ with the boundary values of $f$. For a special holomorphic
function $\vp,$ the present paper gives the necessary and
sufficient condition on $\vp,$ such that $f$ is uniquely
extremal among the class. Further, for a general holomorphic
function $\vp,$ the authors suggest the models of the best
possible growth conditions on $\vp,$ such that $f$ is extremal or
uniquely extremal among the class respectively. |
Keywords: |
Teichm\"uller mapping, Extremality, Unique extremality |
Classification: |
30C70 |
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