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Fefferman’s mapping theorem on almost complex manifolds in complex dimension two

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Abstract.

We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds (see Theorem 1.1). The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinitesimal pseudometric and on the scaling method in almost complex manifolds.

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Authors and Affiliations

  1. C.M.I., 39, rue Joliot-Curie, 13453, Marseille Cedex 13, France

    Bernard Coupet & Hervé Gaussier

  2. U.S.T.L., Cité Scientifique, 59655, Villeneuve d’Ascq Cedex, France

    Alexandre Sukhov

Authors
  1. Bernard Coupet
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  2. Hervé Gaussier
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  3. Alexandre Sukhov
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Correspondence to Hervé Gaussier.

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Mathematics Subject Classification (2000): 32H02,53C15

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Coupet, B., Gaussier, H. & Sukhov, A. Fefferman’s mapping theorem on almost complex manifolds in complex dimension two. Math. Z. 250, 59–90 (2005). https://doi.org/10.1007/s00209-004-0736-y

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