Abstract
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 \((-1,1)\times \mathbb {R}\). 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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Communicated by Andreas Cap.
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Marković, M. On holomorphic functions on negatively curved manifolds. Monatsh Math 196, 851–860 (2021). https://doi.org/10.1007/s00605-021-01625-6
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DOI: https://doi.org/10.1007/s00605-021-01625-6
Keywords
- Holomorphic mappings on complex manifolds
- Modulus and the real part of a holomorphic function
- Hyperbolic distance
- Bergman distance
- Negatively curved manifolds
- Ricci curvature