Extremal quasiconformal mappings with given boundary correspondence

1979 ◽  
Vol 19 (4) ◽  
pp. 671-678 ◽  
Author(s):  
B. G. Sheretov
Keyword(s):  
Quasiconformal Mappings ◽  
Boundary Correspondence

scholarly journals The boundary correspondence under quasiconformal mappings

1956 ◽  
Vol 96 (0) ◽  
pp. 125-142 ◽  
Author(s):  
A. Beurling ◽  
L. Ahlfors
Keyword(s):  
Quasiconformal Mappings ◽  
Boundary Correspondence

scholarly journals Unique extremality, local extremality and extremal non-decreasable dilatations

2007 ◽  
Vol 75 (3) ◽  
pp. 321-329 ◽  
Author(s):  
Guowu Yao
Keyword(s):  
Quasiconformal Mapping ◽  
Unit Circle ◽  
Quasiconformal Mappings ◽  
Boundary Correspondence

Given a quasi-symmetric self-homeomorphism h of the unit circle Sl, let Q(h) be the set of all quasiconformal mappings with the boundary correspondence h. In this paper, it is shown that there exists certain quasi-symmetric homeomorphism h, such that Q(h) satisfies either of the conditions,(1) Q(h) admits a quasiconformal mapping that is both uniquely locally-extremal and uniquely extremal-non-decreasable instead of being uniquely extremal;(2) Q(h) contains infinitely many quasiconformal mappings each of which has an extremal non-decreasable dilatation.An infinitesimal version of this result is also obtained.

scholarly journals On A Property of the Boundary Correspondence under Quasiconformal Mappings

1960 ◽  
Vol 16 ◽  
pp. 185-188 ◽  
Author(s):  
Kazuo Ikoma
Keyword(s):  
Quasiconformal Mapping ◽  
Logarithmic Capacity ◽  
Quasiconformal Mappings ◽  
Maximal Dilatation ◽  
Capacity Zero ◽  
Boundary Correspondence

Let w = f(z) be a quasiconformal mapping, in the sense of Pfluger [5]-Ahlfors [1], with maximal dilatation K, which will be simply referred to a K-QC mapping. As is well known, any K-QC mapping w = f(z) of Im z > 0 onto Im w > 0 can be extended to a homeomorphism from Im z ≧ 0 onto Im w ≧ 0 and hence it transforms any set of logarithmic capacity zero on Im z = 0 into a set with the same property on Im w = 0.

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