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Approximating <Emphasis Type="Italic">J</Emphasis>-holomorphic curves by holomorphic ones

Authors:	Email author" target="_blank">Tristan?Riviére Email author

Institution:	(1) Department of Mathematics, H66 32.5, Rämistr. 101, 8092 Zürich, Switzerland

Abstract:	Given an almost complex structure J in a cylinder of $\mathbb{R}^{2p}$ (p > 1) together with a compatible symplectic form $\omega$ and given an arbitrary J-holomorphic curve $\Sigma$ without boundary in that cylinder, we construct an holomorphic perturbation of $\Sigma$ , for the canonical complex structure J ₀ of $\mathbb{R}^{2p}$ , such that the distance between these two curves in W ^1,2 and $L^\infty$ norms, in a sub-cylinder, are controled by quantities depending on J, $\omega$ and by the area of $\Sigma$ only. These estimates depend neither on the topology nor on the conformal class of $\Sigma$ . They are key tools in the recent proof of the regularity of 1-1 integral currents in RT].Received: 2 October 2003, Accepted: 18 November 2003, Published online: 25 February 2004

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