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The range of holomorphic maps at boundary points

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Abstract

We prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains. That is, we prove that the local image of a holomorphic map \(f{:\,}D\rightarrow D'\) close to a boundary regular contact point \(p\in \partial D\) where the Jacobian is bounded away from zero along normal non-tangential directions has to eventually contain every cone (and more generally every region which is Kobayashi asymptotic to a cone) with vertex at \(f(p)\).

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Authors and Affiliations

  1. Dipartimento Di Matematica, Università Di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133 , Rome, Italy

    Filippo Bracci

  2. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 , Trondheim, Norway

    John Erik Fornæss

Authors
  1. Filippo Bracci
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  2. John Erik Fornæss
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Correspondence to Filippo Bracci.

Additional information

Partially supported by the ERC grant “HEVO—Holomorphic Evolution Equations” n. 277691.

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Bracci, F., Fornæss, J.E. The range of holomorphic maps at boundary points. Math. Ann. 359, 909–927 (2014). https://doi.org/10.1007/s00208-014-1028-4

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  • DOI: https://doi.org/10.1007/s00208-014-1028-4

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