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Extension of a holomorphic curve in $B^4$ to one in $\mathbb{C}P^2$

Let $B^4$ be the closed unit ball in $\mathbb{C}^2$ and $J$ an almost complex structure sufficiently closed to the standard complex structure on $\mathbb{C}^2$ in the $C^0$-topology. Let $u \colon S \...
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