Holomorphic curves at one point
Symplectic Geometry
2012-11-27 v1
Abstract
Let M be a closed symplectic manifold with a compatible almost complex structure J. We prove that for a point p in M and E>0, if v is a non-constant J-holomorphic curve with symplectic area smaller than E, then the number of the pre-images of p is bounded, and the bound is independent of v. We also provide a uniform Hofer's energy bound for J-holomorphic curves in M\p based on the symplectic area. Using these two results we compactify the moduli space of J-holomorphic curves in M by adding holomorphic buildings at the point p.
Cite
@article{arxiv.1211.5732,
title = {Holomorphic curves at one point},
author = {Erkao Bao},
journal= {arXiv preprint arXiv:1211.5732},
year = {2012}
}