Timeline for Why are there no wild arcs in the plane?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 24, 2011 at 1:29 | comment | added | Bill Thurston | Dennis Sullivan found a simple way to construct a map from the boundary of the convex hull of a simply-connected domain to the Poincaré metric on a simply-connected domain that has a bounded bi-Lipschitz constant. David Epstein and Al Marden subsequently gave a very detailed and explicit construction, with an explicit constant. The natural conjecture (or at least a conjecture that is attributed to me) was that the best quasiconformal constant should be 2, but this was disproved: cf. Epstein, Marden and Markovic, Annals of Math 159 (2004) pp 305--336. | |
| Mar 22, 2011 at 7:46 | comment | added | Greg Kuperberg | Is there a more direct relation between these two proofs, other than that they end in a similar way? E.g., is there a correspondence or a relation between the conformal structure on the Jordan domain at infinity, and the hyperbolic structure on the pleated surface? | |
| Mar 8, 2011 at 10:54 | vote | accept | Jim Conant | ||
| Mar 8, 2011 at 4:18 | history | answered | Bill Thurston | CC BY-SA 2.5 |