Quasiconformal mappings and singularity of boundary distortion
| dc.creator | Nieminen, Tomi | |
| dc.creator | Uriarte-Tuero, Ignacio | |
| dc.date | 2008-02-17 | |
| dc.date.accessioned | 2026-07-07T09:21:26Z | |
| dc.date.available | 2026-07-07T09:21:26Z | |
| dc.description | We extend a well-known theorem by Jones and Makarov [JM] on the singularity of boundary distortion of planar conformal mappings. We use a different technique to recover the previous result and, moreover, generalize the result for quasiconformal mappings of the unit ball $\B^n\subset \mathbb{R}^n$, $n\ge 2$. We also establish an estimate on the Hausdorff (gauge) dimension of the boundary of the image domain outside an exceptional set of given size on the sphere $\partial \B^n$. Furthermore, we show that this estimate is essentially sharp. [JM] P. W. Jones and N. Makarov: Density properties of harmonic measure. Ann. Math. 142 (1995), 427--455. | |
| dc.description | 13 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0802.2356 | |
| dc.identifier | http://arxiv.org/abs/0802.2356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155025 | |
| dc.subject | Complex Variables | |
| dc.subject | 30C65 | |
| dc.title | Quasiconformal mappings and singularity of boundary distortion | |
| dc.type | text |