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Neighborhood of an Embedded J-Holomorphic Disc

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Abstract

We study the deformation space of an embedded J-holomorphic disc D in an almost complex surface (X,J). Every such J is shown to be equivalent to a small deformation of a certain model structure J β along D, where β : D→ℂ is a complex valued function whose modulus |β| is a biholomorphic invariant. Furthermore, we find a nonlinear invertible operator mapping the space of all small J-holomorphic deformations of the given J-holomorphic disc onto the space of small holomorphic deformations of the standard disc in ℂ2.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Uroš Kuzman

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  1. Uroš Kuzman
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Correspondence to Uroš Kuzman.

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Communicated by Steven Bell.

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Kuzman, U. Neighborhood of an Embedded J-Holomorphic Disc. J Geom Anal 20, 168–176 (2010). https://doi.org/10.1007/s12220-009-9094-7

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  • DOI: https://doi.org/10.1007/s12220-009-9094-7

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