Combinatorically Prescribed Packings and Applications to Conformal and Quasiconformal Maps
| dc.creator | Schramm, Oded | |
| dc.date | 2007-09-05 | |
| dc.date.accessioned | 2026-07-07T08:27:47Z | |
| dc.date.available | 2026-07-07T08:27:47Z | |
| dc.description | The Andreev-Thurston Circle Packing Theorem is generalized to packings of convex bodies in planar simply connected domains. This turns out to be a useful tool for constructing conformal and quasiconformal mappings with interesting geometric properties. We attempt to illustrate this with a few results about uniformizations of finitely connected planar domains. For example, the following variation of a theorem by Courant, Manel and Shiffman is proved and generalized. If $G$ is an $n+1$-connected bounded planar domain, $H$ is a simply connected bounded planar domain, and $P_1,P_2,...,P_n$ are (compact) planar convex bodies, then sets $P_j'$ can be found so that $G$ is conformally equivalent to $H-\cup_{j=1}^n P_j'$, and each $P_j'$ is either a point, or is positively homothetic to $P_j$. | |
| dc.description | Modified version of PhD thesis from 1990 | |
| dc.identifier | https://arxiv.org/abs/0709.0710 | |
| dc.identifier | http://arxiv.org/abs/0709.0710 | |
| dc.identifier | Ph. D. thesis. Princeton University (1990) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137388 | |
| dc.subject | Complex Variables | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 52C15; 30C20 | |
| dc.title | Combinatorically Prescribed Packings and Applications to Conformal and Quasiconformal Maps | |
| dc.type | text |