Reflection principle and \(J\)-complex curves with boundary on totally real immersions. (English) Zbl 1025.32024

Summary: We prove a version of the reflection principle for pseudoholomorphic disks with boundary on totally real submanifolds in almost-complex manifolds. Furthermore, we give a proof of the Gromov compactness theorem for pseudoholomorphic curves with boundary on immersed totally real submanifolds. As a corollary we show that a complex disk can be attached to any immersed Lagrangian submanifold with only transversal double points in a complex linear space.


32Q65 Pseudoholomorphic curves
53D12 Lagrangian submanifolds; Maslov index
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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