On holomorphic functions on negatively curved manifolds

@article{Markovic2021OnHF,
  title={On holomorphic functions on negatively curved manifolds},
  author={Marijan Markovic},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2021}
}
  • Marijan Markovic
  • Published 21 September 2021
  • Mathematics
  • Monatshefte für Mathematik
Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a Kähler manifold with the Ricci curvature bounded from below by −1 is contractive with respect to the distance on the manifold and the hyperbolic distance on (−1, 1) inhered from the domain (−1, 1)×R. Moreover, in the case of bounded holomorphic functions we prove that the modulus is contractive with respect to the distance on the manifold and the hyperbolic distance on the unit disk. 

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