J-holomorphic curves with boundary in bounded geometry
Symplectic Geometry
2017-02-10 v2 Differential Geometry
Abstract
The fundamental properties of -holomorphic maps depend on two inequalities: The gradient inequality gives a pointwise bound on the differential of a -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.
Keywords
Cite
@article{arxiv.1311.7484,
title = {J-holomorphic curves with boundary in bounded geometry},
author = {Yoel Groman and Jake P. Solomon},
journal= {arXiv preprint arXiv:1311.7484},
year = {2017}
}
Comments
38 pages; main theorem now requires compatibility of $J$ along $L$ and bounds on third derivatives of $J$; added Section 3.3.2; corrected minor errors