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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.

MSC:

32Q65 Pseudoholomorphic curves
53D12 Lagrangian submanifolds; Maslov index
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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[1] DOI: 10.1007/BF02684599 · Zbl 0181.48803
[2] DOI: 10.1007/BF01388806 · Zbl 0592.53025
[3] Gromov M., Proc. Int. Congr. Math. 1986 pp 1– (1987)
[4] Kontsevich M., Netherland. Birkhäuser Prog. Math. 129 pp 335– (1995)
[5] DOI: 10.1007/BF02101490 · Zbl 0853.14020
[6] Mumford D., Proc. Amer. Math. Soc. 28 pp 289– (1971)
[7] Parker T., J. Diff. Geom. 44 pp 595– (1996) · Zbl 0874.58012
[8] DOI: 10.1007/BF02921330 · Zbl 0759.53023
[9] DOI: 10.2307/1971131 · Zbl 0462.58014
[10] Sikorav J.-C., eds M. Audin and J. Lafontaine, Birkhäuser, Progress in Mathematics 117 pp 165–
[11] Sikorav J.-C., Trav. Cours 25 pp 95– (1987)
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