A thickthin decomposition of $J$holomorphic curves
Abstract
We show the existence of a thick thin decomposition of the domain of a pseudo holomorphic curve with boundary. The geometry of the thick part is bounded uniformly in the energy. Furthermore, in the thick part, there is a uniform bound on the differential which is exponential in the energy. The thin part consists of annuli of small energy the number of which is at most linear in the energy and genus. The decomposition can be seen as a quantitative version of Gromov compactness which applies before passing to the limit.
 Publication:

arXiv eprints
 Pub Date:
 November 2013
 DOI:
 10.48550/arXiv.1311.7564
 arXiv:
 arXiv:1311.7564
 Bibcode:
 2013arXiv1311.7564G
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Differential Geometry;
 32Q65 (Primary) 53D12;
 53D40;
 53D45 (Secondary)
 EPrint:
 49 pages, 2 figures, shares some basic definitions and a lemma with arXiv:1210.4001