|
|
| |
| FEASIBILITY OF THE REICH PROCEDURE IN THE DECOMPOSITION OF PLANE QUASICONFORMAL MAPPINGS |
| |
Citation： |
Lai Wancai.FEASIBILITY OF THE REICH PROCEDURE IN THE DECOMPOSITION OF PLANE QUASICONFORMAL MAPPINGS[J].Chinese Annals of Mathematics B,1995,16(1):109~118 |
| Page view： 907
Net amount： 624 |
Authors： |
Lai Wancai; |
|
|
| Abstract： |
In the decomposition problems, studied by Reich, of quasiconformal self
mappings of the unit disc which keep the boundary points fixed, the
construction of the first one requires the application of the
Hahn-Banach theorem (so it is abstract) and it is only a variational
decomposition (a small weight one), and that of the second one avoids
the Hahn-Banach theorem and gets rid of the restriction to the
variational decomposition. But the success of the second decomposition
procedure (the Reich procedure) is guaranteed only when minimal maximal
dilatation $K(f)$ is sufficiently small. Therefore, it can not guarantee
even a variational decomposition. Huang Xinzhong then proved that the
inverse Reich procedure was successful for any $K(f)$. But the inverse
Reich procedure is not so natural as the Reich procedure and the
corresponding decomposition can not replace the first one. It is still
an open problem whether the Reich procedure is successful for any
$K(f)$. The present paper gives an affirmative answer to this problem. |
Keywords： |
Quasiconformal mapping, Decomposition, Reich's procedure. |
Classification： |
30C62 |
|
|
Download PDF Full-Text
|
|
|
|
