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arXiv · 2312.15232

On Harnack inequality and harmonic Schwarz lemma

Rahim Kargar
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Abstract

In this paper, we study the $(s, C(s))$-Harnack inequality in a domain $G\subset \mathbb{R}^n$ for $s\in(0,1)$ and $C(s)\geq1$ and present a series of inequalities related to $(s, C(s))$-Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under $K$-quasiconformal and $K$-quasiregular mappings, where $K\geq 1$. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz-Pick estimate for a real-valued harmonic function.

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Rahim Kargar. 2023-12-23. On Harnack inequality and harmonic Schwarz lemma. https://doi.org/10.4153/s0008439524000298

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