A+ CATEGORY SCIENTIFIC UNIT

Normal pseudoholomorphic curves

Volume 101 / 2011

Fathi Haggui, Adel Khalfallah Annales Polonici Mathematici 101 (2011), 55-65 MSC: 32Q45, 32Q60, 32Q65. DOI: 10.4064/ap101-1-6

Abstract

First, we give some characterizations of $J$-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold follows from relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi, Kiernan and Joseph–Kwack in the standard complex case.

Authors

  • Fathi HagguiInstitut préparatoire aux études d'ingénieur
    rue Ibn-Eljazzar
    5019 Monastir, Tunisie
    e-mail
  • Adel KhalfallahInstitut préparatoire aux études d'ingénieur
    rue Ibn-Eljazzar
    5019 Monastir, Tunisie
    e-mail

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