J-holomorphic curves with boundary in bounded geometry

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Abstract

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.

Original languageAmerican English
Pages (from-to)767-809
Number of pages43
JournalJournal of Symplectic Geometry
Volume14
Issue number3
DOIs
StatePublished - 2016

Bibliographical note

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© by International Press of Boston, Inc. All rights reserved.

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