2011/05/24 by Manzi Huang, Yaxiang Li, Huang, Manzi +5
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1105.4684
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D\varsubsetneq E and D'\varsubsetneq E' are domains, that f: D→ D' is an (M,C)-CQH homeomorphism, and that D is uniform. The main aim of this paper is to prove that D' is a uniform domain if and only if f extends to a homeomorphism f: D→ D' and 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.