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Can you give me a reference for the proof of the filling by holomorphic disks method, besides Bishop's original paper?

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I really don't understand what proof you're looking for, but maybe you can find it here: Y. Eliashberg: Filling by holomorphic discs and its applications, in Geometry of low-dimensional manifolds, 2 (Durham, 1989), 45–67, London Math. Soc. Lecture Note Ser., 151, Cambridge Univ. Press, Cambridge, 1990. –  Oldřich Spáčil Mar 24 at 14:26

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