Abstract
For any 1 ≤ a ≤ n, there is a compact set E ⊂ ℝn of (Hausdorff) dimension α whose dimension cannot be lowered by any quasiconformal map f : ℝn → ℝn. We conjecture that no such set exists in the case α < 1. More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3361-3367 |
| Number of pages | 7 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 128 |
| Issue number | 11 |
| DOIs | |
| State | Published - 2000 |
| Externally published | Yes |
Keywords
- Generalized modulus
- Hausdorff dimension
- Quasiconformal maps
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics