×

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.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/BF02684599 · Zbl 0181.48803 · doi:10.1007/BF02684599
[2] DOI: 10.1007/BF01388806 · Zbl 0592.53025 · doi:10.1007/BF01388806
[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 · doi:10.1007/BF02101490
[6] Mumford D., Proc. Amer. Math. Soc. 28 pp 289– (1971)
[7] Parker T., J. Diff. Geom. 44 pp 595– (1996) · Zbl 0874.58012 · doi:10.4310/jdg/1214459224
[8] DOI: 10.1007/BF02921330 · Zbl 0759.53023 · doi:10.1007/BF02921330
[9] DOI: 10.2307/1971131 · Zbl 0462.58014 · doi:10.2307/1971131
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.