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J-holomorphic curves with boundary in bounded geometry

Authors
  • Groman, Yoel
  • Solomon, Jake P.
Type
Preprint
Publication Date
Oct 02, 2014
Submission Date
Nov 29, 2013
Identifiers
arXiv ID: 1311.7484
Source
arXiv
License
Yellow
External links

Abstract

The fundamental properties of $J$-holomorphic maps 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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