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Jan 29, 2023 at 21:15 vote accept John Pardon
Jan 29, 2023 at 21:15 answer added John Pardon timeline score: 3
Sep 5, 2015 at 19:38 comment added BS. It seems that you have found the answer, but I thought of a simpler approach (maybe wrong): what about the subset of $D^2\times D^2$ defined by $g(x)=f(y)$ ? It should be complex analytic (for the standard complex structure), and your assumption amounts to say that it contains the graph of your $\phi:U\to V$. Maybe the assumption of smoothness of boundaries of $U,V$ and local structure of complex analytic curves would suffice to conclude ?
Sep 4, 2015 at 12:55 comment added John Pardon It looks like Theorem 2.83 in Chris Wendl's book arxiv.org/abs/1011.1690v2 might be what I'm looking for.
Sep 4, 2015 at 8:44 history edited John Pardon CC BY-SA 3.0
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Sep 4, 2015 at 7:57 answer added Nikolaki timeline score: 1
Sep 3, 2015 at 13:25 history asked John Pardon CC BY-SA 3.0