Timeline for Analytic implicit function theorem
Current License: CC BY-SA 3.0
4 events
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| Aug 22, 2011 at 12:20 | comment | added | Henri | @unknowngoogle: You're perfectly right for the general $n$-dimensional case. As for the second comment, I agree too, this is more or less the meaning of my last sentence in the answer. So, thanks! | |
| Aug 22, 2011 at 11:24 | comment | added | Qfwfq | If I don't misremember the analytic implicit function thm should be a relatively 'formal' consequence of the analytic inverse function thm. | |
| Aug 22, 2011 at 11:19 | comment | added | Qfwfq | This is also true in higher dimention, at least for manifolds (nonsingular analytic spaces). The $\mathcal{C}^1$ inverse function theorem + the fact that, loosely, if the differential belongs to $\mathrm{GL}(n,\mathbb{C})\subset\mathrm{GL}(2n,\mathbb{R})$, also its inverse does. | |
| Aug 22, 2011 at 9:12 | history | answered | Henri | CC BY-SA 3.0 |