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For questions about or involving complex manifolds.

5 votes
Accepted

(Contradiction) All symplectic manifolds are holomorphic

The comments of @JHM and @Ivan Solonenko contain an answer to OP's question. (1) The OP is correct that $j_0:=\phi_* \circ J \circ \phi^{-1}_*$ is an almost-complex structure on the image $V:=\phi(U) …
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3 votes

Is a non-compact Riemann surface an open subset of a compact one ?

Useful references for your question are Robert Brooks' "Platonic surfaces" and Dan Mangoubi's "Conformal Extension of Metrics of Negative Curvature" (both on arxiv). I emailed Luca Migliorini requ …
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