On bilipschitz extensions in real Banach spaces

الأصل · EN

Suppose that E and E' denote real Banach spaces with dimension at least 2, that D=E and D'=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.