A foliation of the ball by complete holomorphic discs


We show that the open unit ball \(\mathbb {B}^n\) of \(\mathbb {C}^n\)\((n>1)\) admits a nonsingular holomorphic foliation by complete properly embedded holomorphic discs.

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A. Alarcón is supported by the State Research Agency (SRA) and European Regional Development Fund (ERDF) via the Grant no. MTM2017-89677-P, MICINN, Spain. F. Forstnerič is supported by the research program P1-0291 and the research Grant J1-9104 from ARRS, Republic of Slovenia.

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Correspondence to Antonio Alarcón.

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Alarcón, A., Forstnerič, F. A foliation of the ball by complete holomorphic discs. Math. Z. 296, 169–174 (2020). https://doi.org/10.1007/s00209-019-02430-6

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  • Riemann surface
  • Holomorphic disc
  • Foliation
  • Complete Riemannian manifold

Mathematics Subject Classification

  • 32B15
  • 32H02
  • 32M17
  • 53C12