TITLE

# ApproximatingJ-holomorphic curves by holomorphic ones

AUTHOR(S)
Riviére, Tristan
PUB. DATE
November 2004
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2004, Vol. 21 Issue 3, p273
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Given an almost complex structure J in a cylinder of R2p (p > 1) together with a compatible symplectic form Ï‰ and given an arbitrary J-holomorphic curve 2 without boundary in that cylinder, we construct an holomorphic perturbation of Î£, for the canonical complex structure J0 of R2p, such that the distance between these two curves in W1,2 and Lâˆž norms, in a sub-cylinder, are controled by quantities depending on J, Ï‰ and by the area of 2 only. These estimates depend neither on the topology nor on the conformal class of Î£. They are key tools in the recent proof of the regularity of 1-1 integral currents in [RT].
ACCESSION #
14509085

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