Quasisymmetric embeddings in Euclidean spaces
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- by Jussi Väisälä PDF
- Trans. Amer. Math. Soc. 264 (1981), 191-204 Request permission
Abstract:
We consider quasi-symmetric embeddings $f:G \to {R^n}$, $G$ open in ${R^p}$, $p \leqslant n$. If $p = n$, quasi-symmetry implies quasi-conformality. The converse is true if $G$ has a sufficiently smooth boundary. If $p < n$, the Hausdorff dimension of $fG$ is less than $n$. If $fG$ has a finite $p$-measure, $f$ preserves the property of being of $p$-measure zero. If $p < n$ and $n \geqslant 3$, ${R^n}$ contains a quasi-symmetric $p$-cell which is topologically wild. We also prove auxiliary results on the relations between Hausdorff measure and Čech cohomology.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 264 (1981), 191-204
- MSC: Primary 30C60; Secondary 28A75, 54C25, 54E40, 57N45
- DOI: https://doi.org/10.1090/S0002-9947-1981-0597876-7
- MathSciNet review: 597876