David maps and Hausdorff Dimension
| dc.creator | Zakeri, S. | |
| dc.date | 2002-12-07 | |
| dc.date.accessioned | 2026-07-07T04:53:36Z | |
| dc.date.available | 2026-07-07T04:53:36Z | |
| dc.description | David maps are generalizations of classical planar quasiconformal maps for which the dilatation is allowed to tend to infinity in a controlled fashion. In this note we examine how these maps distort Hausdorff dimension. We show \vs {enumerate} [$\bullet$] Given $α$ and $β$ in $[0,2]$, there exists a David map $ϕ:\CC \to \CC$ and a compact set $Λ$ such that $\Hdim Λ=α$ and $\Hdim ϕ(Λ)=β$. \vs [$\bullet$] There exists a David map $ϕ:\CC \to \CC$ such that the Jordan curve $Γ=ϕ(\Sen)$ satisfies $\Hdim Γ=2$.\vs {enumerate} One should contrast the first statement with the fact that quasiconformal maps preserve sets of Hausdorff dimension 0 and 2. The second statement provides an example of a Jordan curve with Hausdorff dimension 2 which is (quasi)conformally removable. | |
| dc.description | 15 Pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0212106 | |
| dc.identifier | http://arxiv.org/abs/math/0212106 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65918 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | Stony Brook IMS #2002/5 | |
| dc.title | David maps and Hausdorff Dimension | |
| dc.type | text |