ApproximatingJ-holomorphic curves by holomorphic ones

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


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