Timeline for Blackbox Theorems
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2012 at 17:47 | comment | added | Johannes Ebert | The ration #{people who quote the theorem on a daily basis} / #{people who know the details of the proof offhand} is very high, so it is a perfect example of a blackbox theorem. | |
| Jun 26, 2012 at 17:40 | comment | added | Johannes Ebert | @HeWhoHungers: I agree that the proof in Demailly's book is marvellous and elegant, but it is neither easy or short in any sense. I talked about exactly this proof in a lecture course on Teichmüller theory some years ago, addressing an audience of very bright graduate students. I needed 3 or 4 hours to communicate the proof and I remember it to be a tour de force, both for me and the audience. Even if you take the advanced tools for granted (as I did), the details (many of which are thrown under the carpet in the book) are very, very subtle. | |
| Jun 18, 2012 at 16:25 | comment | added | Malik Younsi | The only proof I've seen is the one with the Green's function. Thank you for the reference! | |
| Jun 16, 2012 at 1:24 | comment | added | HeWhoHungers | The standard proof of the Uniformization theorem with the Green's function, while rather involved, shouldn't really surpass the ability of most who come across it. There also exists a short and elegant proof that uses certain rather more advanced tools: the Mayer-Vietoris sequence and the celebrated Newlander-Nirenberg theorem. But NN for surfaces is just the existence of isothermal coordinates, which is much simpler to prove. This proof can be found in Demailly's "Complex Analytic and Differential Geometry" (available at www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf). | |
| Jun 14, 2012 at 1:36 | history | answered | Malik Younsi | CC BY-SA 3.0 |