Schwarz lemmas via the pluricomplex Green's function

Abstract

We prove a version of the Schwarz lemma for holomorphic mappings from the unit disk into the symmetric product of a Riemann surface. Our proof is function-theoretic and self-contained. The main novelty in our proof is the use of the pluricomplex Green's function. We also prove several other Schwarz lemmas using this function.

arXiv commentLemma 22 has been deleted. Some minor fixes

References in corpus (6)

• Extremal holomorphic maps and the symmetrised bidisc
• Some new observations on interpolation in the spectral unit ball
• Nonisotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick problem
• Proper holomorphic mappings onto symmetric products of a Riemann surface
• The 3-point spectral Pick interpolation problem and an application to holomorphic correspondences
• Function theoretic properties of symmetric powers of complex manifolds