Geodesic
On Harnack inequality and harmonic Schwarz lemma
Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 940-954

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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 $C(s)\geq 1$ 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.
DOI : 10.4153/S0008439524000298
Mots-clés : Harnack inequality, Harnack metric, hyperbolic metric, modulus metric, Schwarz lemma 
Kargar, Rahim. On Harnack inequality and harmonic Schwarz lemma. Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 940-954. doi: 10.4153/S0008439524000298
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     title = {On {Harnack} inequality and harmonic {Schwarz} lemma},
     journal = {Canadian mathematical bulletin},
     pages = {940--954},
     year = {2024},
     volume = {67},
     number = {4},
     doi = {10.4153/S0008439524000298},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000298/}
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