2012/11/09 by Huang, Manzi, Li, Yaxiang
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1211.2022
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D\not=E and D'\not=E' are bounded domains with connected boundaries, that f: D→ D' is an M-QH homeomorphism, and that D' is uniform. The main aim of this paper is to prove that f extends to a homeomorphism D→ D' and f|∂ D is bilipschitz if and only if f is bilipschitz in D. The answer to some open problem of Väisälä is affirmative under an natural additional condition.