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On the Distortion Theorem for Quasiconformal Mappings with Fixed Boundary Values

✍ Scribed by Huang Xinzhong; Nak Eun Cho

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
51 KB
Volume
256
Category
Article
ISSN
0022-247X

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✦ Synopsis

For a planar domain ⍀ with at least three boundary points and the ⍀ hyperbolic metric of ⍀ with constant curvature y1, G. J. Martin poses a problem that asks, if f is a K-quasiconformal self-homeomorphism of ⍀ with boundary Ε½ Ε½ .. values given by the identity mapping, whether z, f z F log K holds for ⍀ Ε½ . z, f z g ⍀. In this note, we give a negative answer to this question.

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A question of the existence of fiolutions of boundary-value problems for differential equations with parameter was considered by many authors, see [1]-[3] and [5]-[9]. The analogous problems for differential equations with a deviated argument was discussed in [8] and [3]. The purpose of this paper