Timeline for Riemann mapping theorem and smoothness on the boundary
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 10, 2011 at 10:24 | comment | added | André Henriques | I'm perfectly happy with an argument that uses the Laplace operator. But why not use the $\bar \partial$ operator directly? Isn't this regularity thing a common feature of all elliptic differential operators? | |
| Dec 9, 2011 at 10:45 | comment | added | Igor Rivin | I will try to find another reference (though I suspect the "regularity theory for the Laplace operator" cannot be escaped entirely, since this result is clearly a part of it...) | |
| Dec 9, 2011 at 10:28 | comment | added | André Henriques | After having a closer look at that article, I'm not longer very satisfied by it. The argument I care about is entirely contained in the last page (one can safely disregard everything that comes before). The assumption that the boundary is $C^\infty$ is only used implicitly in the sentence "by the regularity theory of the Laplace operator". Also, I can't follow the last argument (last line of the paper): if you know that $|f(z)|^2$ is smooth, how do you conclude that $f(z)$ is smooth? | |
| Dec 7, 2011 at 20:53 | vote | accept | André Henriques | ||
| Dec 10, 2011 at 10:40 | |||||
| Dec 4, 2011 at 12:10 | history | answered | Igor Rivin | CC BY-SA 3.0 |