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Reconstruction of domains from their groups of quasiconformal autohomeomorphisms

✍ Scribed by Vladimir Goldshtein; Matatyahu Rubin

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 849 KB
Volume: 5
Category: Article
ISSN: 0926-2245
DOI: 10.1016/0926-2245(95)92846-w

No coin nor oath required. For personal study only.

✦ Synopsis

For an open set U c Iw", let &C(U) denote the group of all quasiconformal homeomorphism of U. The following is our first main result. Let U C iw" and V c R" be open, and suppose that r is a group isomorphism between QC(U) and &C(V). Then there is a quasiconformal homeomorphism 9 from U onto V such that y induce r. That is, for every f E &C(ri): r(f)=~ofOu-l_

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