naa a22 4500 510782183 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0043-6 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0043-6 On quasimöbius maps in real Banach spaces [Elektronische Daten] [M. Huang, Y. Li, M. Vuorinen, X. Wang] Suppose that E and E′ denote real Banach spaces with dimension at least 2, that D $$ \subseteq $$ E and D′ $$ \subseteq $$ 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 $$\overline f :\overline D \to {\overline D ^\prime }$$ and $$\overline f $$ is η-QM relative to ∂D. This result shows that the answer to one of the open problems raised by Väisälä from 1991 is affirmative. Hebrew University Magnes Press, 2013 Huang M. Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Hunan Normal University, 410081, Changsha, Hunan, P. R. China aut Li Y. Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Hunan Normal University, 410081, Changsha, Hunan, P. R. China aut Vuorinen M. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland aut Wang X. Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Hunan Normal University, 410081, Changsha, Hunan, P. R. China aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 467-486 0021-2172 198:1<467 2013 198 11856 https://doi.org/10.1007/s11856-013-0043-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0043-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang M. Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Hunan Normal University, 410081, Changsha, Hunan, P. R. China aut NATIONALLICENCE 700 1- Li Y. Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Hunan Normal University, 410081, Changsha, Hunan, P. R. China aut NATIONALLICENCE 700 1- Vuorinen M. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland aut NATIONALLICENCE 700 1- Wang X. Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP), Hunan Normal University, 410081, Changsha, Hunan, P. R. China aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 467-486 0021-2172 198:1<467 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer