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Mathematics > Complex Variables

arXiv:1812.10337 (math)
[Submitted on 26 Dec 2018 (v1), last revised 9 Sep 2019 (this version, v3)]

Title:Schwarz lemmas via the pluricomplex Green's function

Authors:Jaikrishnan Janardhanan
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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.
Comments: Lemma 22 has been deleted. Some minor fixes
Subjects: Complex Variables (math.CV)
MSC classes: 32H15, 32H20, 32U35
Cite as: arXiv:1812.10337 [math.CV]
  (or arXiv:1812.10337v3 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1812.10337
Related DOI: https://doi.org/10.1007/s12220-019-00232-0

Submission history

From: Jaikrishnan Janardhanan [view email]
[v1] Wed, 26 Dec 2018 15:06:34 UTC (17 KB)
[v2] Tue, 8 Jan 2019 12:43:20 UTC (18 KB)
[v3] Mon, 9 Sep 2019 09:42:37 UTC (17 KB)
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