2021/09/21 by Markovic, Marijan
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.10264
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.