2013/11/29 by Yoel Groman, Groman, Yoel
Mathematics · #32Q65 (Primary) 53D12 #53D40 #53D45 (Secondary) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:32Q65 #msc:53D12 #msc:53D40 #msc:53D45
paper · pdf · doi:10.48550/arxiv.1311.7564
49 pages, 2 figures, shares some basic definitions and a lemma with arXiv:1210.4001
arxiv created 2013/11/29 · openalex publication_date 2013/11/29 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.