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Sep 9, 2020 at 0:37 comment added Rohil Prasad It's not exactly what you're looking for, but Joel Fish's "Target-local Gromov compactness theorem" (arxiv.org/abs/0912.4435) gives a Gromov compactness theorem for $J$-holomorphic curves with boundary that live inside a manifold with boundary. It relies on the interpretation of $J$-holomorphic curves as surfaces satisfying an inhomogeneous mean curvature equation.
Sep 8, 2020 at 18:56 history asked Quarto Bendir CC BY-SA 4.0