On Quasimöbius Maps in Real Banach Spaces

: M Huang, Y Li, M Vuorinen, X Wang

Publisher: HEBREW UNIV MAGNES PRESS

: JERUSALEM; PO BOX 39099, JERUSALEM 91390, ISRAEL

: 2013

: Israel Journal of Mathematics

: Isr.J.Math.

: 1

: 198

: 1

: 467

: 486

: 20

: 0021-2172

DOI: https://doi.org/10.1007/s11856-013-0043-6

: http://api.elsevier.com/content/abstract/scopus_id:84883821449

Suppose that E and E' denote real Banach spaces with dimension at least 2, that D not subset of E and D' not subset of E' are domains, that f : D -> D' is an (M, C)-CQH homeomorphism, and that D is uniform. The aim of this paper is to prove that D' is a uniform domain if and only if f extends to a homeomorphism (f) over bar : (D) over bar -> (D) over bar' and (f) over bar is eta-QM relative to partial derivative D. This result shows that the answer to one of the open problems raised by Vaisala from 1991 is affirmative.