Oh, wow, I came in a few minutes ago and found that I was banned for saying "yeah you slow man" to Daminark. I can't make head or tails of this. Finally we have reached the point where I'm being banned for random messages, neither inappropriate with context or without.
I mean he may do concrete things but he apparently views geometric intuition as being somehow at odds with theory. In particular, he griped that it took too long to define categories
It just depends on what "proof" means. Is a picture allowed in how you parse the proof? That's true for topology. I am sure there might be varying cultures in mathematics which have distinct meaning associated to proof.
If you have a complex manifold, presumably it'd also be a real manifold under some canonically derived differential structure, right? If so, how much structure do you lose with that?
Well, if it's compact you know it's bounded on the manifold, which is almost Liouville. I would guess that either charts or analytic continuation (guessing the former) allows us to push toward full power Liouville?
The things I've "seen" in complex analysis are the early results about C-R, real and imaginary parts being harmonic, Cauchy integral theorem/formula and Liouville, singularities, Laurent series, branch stuff, and Christoffel-Schwarz
There's an integrability condition (sort of like Frobenius, Eric — in fact, if you assume real analyticity, it is Frobenius). Look up the Nijenhuis tensor.
I can't classify for $pq$ yet, but I do know thanks to theorems on product sets and so on that $\Bbb Z_p \times \Bbb Z_q$ is one such group (if you meant for $p,q$ to be prime).
