## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Quasi-Symmetric Embeddings in Euclidean Spaces

Jussi Väisälä
Transactions of the American Mathematical Society
Vol. 264, No. 1 (Mar., 1981), pp. 191-204
DOI: 10.2307/1998419
Stable URL: http://www.jstor.org/stable/1998419
Page Count: 14
Preview not available

## Abstract

We consider quasi-symmetric embeddings $f: G \rightarrow R^n, G$ 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 Cech cohomology.

• 191
• 192
• 193
• 194
• 195
• 196
• 197
• 198
• 199
• 200
• 201
• 202
• 203
• 204