Timeline for When are conformal maps holomorphic?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2012 at 12:05 | vote | accept | Grant Rotskoff | ||
| Apr 4, 2012 at 4:57 | comment | added | Michael Greenblatt | The fact that it's conformal is equivalent to a condition on the matrix of first derivatives. If the determinant is nonneegative the condition is the same as the Cauchy-Riemann equations, otherwise the Cauchy-Riemann equations are off by a factor of -1. So if you stipulate the determinant of the Jacobian is nonnegative (orientation is preserved) then it implies holomorphicity (as long as $f$ is $C^1$.) | |
| Apr 4, 2012 at 4:45 | comment | added | Misha | Depends if you allow conformal maps to change the orientation. In any case, you get either just holomorphic or both holomorphic and anti-holomorphic maps. This is a part of any standard complex analysis course. By the way, in the "standard fact" you should also assume that $f$ is nonconstant. | |
| Apr 4, 2012 at 4:21 | answer | added | User3568 | timeline score: 2 | |
| Apr 4, 2012 at 4:05 | history | asked | Grant Rotskoff | CC BY-SA 3.0 |