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Title:
Gromov compactness without boundary estimate
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Abstract:
The usual way to prove compactness of a moduli space of pseudoholomorphic curves with a Lagrangian boundary condition relies on a priori estimate of the Cauchy-Riemann equation. If the Lagrangian submanifold is singular, or if one has a degenerating sequence of Lagrangians, or if we only expect the boundary condition to hold in the limit, it is difficult to obtain a uniform boundary estimate. I will try to explain that to prove compactness one only needs the isoperimetric inequality for paths and the interior estimate. This method will allow us to prove compactness for certain singular Lagrangian boundary conditions and potentially study Floer theory for such objects.
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