On bilipschitz extensions in real Banach spacesReport as inadecuate



 On bilipschitz extensions in real Banach spaces


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Suppose that $E$ and $E$ denote real Banach spaces with dimension at least 2, that $D ot=E$ and $D ot=E$ are bounded domains with connected boundaries, that $f: D\to D$ 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 $\bar \bar{D}\to \bar{D}$ and $\bar{f}|\partial D$ is bilipschitz if and only if $f$ is bilipschitz in $\bar{D}$. The answer to some open problem of V\-ais\-al\-a is affirmative under an natural additional condition.



Author: Manzi Huang; Yaxiang Li

Source: https://archive.org/



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