Compactness for holomorphic curves with switching Lagrangian boundary conditions

We prove a compactness result for holomorphic curves with boundary on an immersed Lagrangian submanifold with clean self-intersection. As an important consequence, we show that the number of intersections of such holomorphic curves with the self-intersection locus is uniformly bounded in terms of the Hofer energy.

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Published 1 January 2010