Sharp nonremovability examples for Hölder continuous quasiregular mappings in the plane
| dc.creator | Clop, Albert | |
| dc.creator | Uriarte-Tuero, Ignacio | |
| dc.date | 2007-10-01 | |
| dc.date.accessioned | 2026-07-07T08:33:16Z | |
| dc.date.available | 2026-07-07T08:33:16Z | |
| dc.description | Let $α\in(0,1)$, $K\geq 1$, and $d=2\frac{1+αK}{1+K}$. Given a compact set $E\subset\C$, it is known that if $\H^d(E)=0$ then $E$ is removable for $α$-Hölder continuous $K$-quasiregular mappings in the plane. The sharpness of the index $d$ is shown with the construction, for any $t>d$, of a set $E$ of Hausdorff dimension $\dim(E)=t$ which is not removable. In this paper, we improve this result and construct compact nonremovable sets $E$ such that $0<\H^d(E)<\infty$. For the proof, we give a precise planar $K$-quasiconformal mapping whose Hölder exponent is strictly bigger than $\frac{1}{K}$, and that exhibits extremal distortion properties. | |
| dc.description | 19 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0710.0234 | |
| dc.identifier | http://arxiv.org/abs/0710.0234 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139067 | |
| dc.subject | Complex Variables | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 30C62,35J15 | |
| dc.title | Sharp nonremovability examples for Hölder continuous quasiregular mappings in the plane | |
| dc.type | text |