Journal of Symplectic Geometry

Volume 14 (2016)

Number 3

$J$-holomorphic curves with boundary in bounded geometry

Pages: 767 – 809



Yoel Groman (ETH Zürich, Switzerland)

Jake P. Solomon (Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel)


The fundamental properties of $J$-holomorphic curves depend on two inequalities: The gradient inequality gives a pointwise bound on the differential of a $J$-holomorphic map in terms of its energy. The cylinder inequality stipulates and quantifies the exponential decay of energy along cylinders of small total energy.We show these inequalities hold uniformly if the geometry of the target symplectic manifold and Lagrangian boundary condition is appropriately bounded.

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