/sci/ - Science & Math

>>11525379
What local perspective, tho?
It's not even a "doesn't Darboux trivialize the local theory" thing, I can't really recall any other results that properly get the title of local, beyond Moser isotopy and Duistermaat-Heckman.
>>11525557
>That is, we can pick a direction along which we can get outside of the half-space, using just the limit definition of the derivative.
I'm not saying it doesn't work, but I will tell you it probably doesn't. Do tell me if you somehow manage to force that out from the definition.
If you want an absolutely elementary proof, >>11522817 probably works, [math]J_h=0[/math] because it's a critical point, but [math]J_g[/math] is an isomorphism and [math]J_f[/math] is nonzero, thus by the chain rule for jacobians we have a contradiction.
Essentially just elementary results.