On Harnack inequality and harmonic Schwarz lemma
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929622309928960 |
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| author | Kargar, Rahim |
| author_facet | Kargar, Rahim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15232 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Harnack inequality and harmonic Schwarz lemma Kargar, Rahim Complex Variables Metric Geometry 30C20, 30C80 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. |
| title | On Harnack inequality and harmonic Schwarz lemma |
| topic | Complex Variables Metric Geometry 30C20, 30C80 |
| url | https://arxiv.org/abs/2312.15232 |