Weighted Yosida Mappings of Several Complex Variables
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909286192381952 |
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| author | Bharti, Nikhil Van Thin, Nguyen |
| author_facet | Bharti, Nikhil Van Thin, Nguyen |
| contents | Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let $φ: [0,\infty)\rightarrow (0,\infty)$ be positive function such that $$γ_r=\sup\limits_{r\leq a<b}\left|(φ(a)-φ(b))/(a-b)\right|\leq C,~r\in (0,\infty),$$ for some $C\in (0,1],$ and $\lim_{r\rightarrow\infty}γ_r=0.$ A holomorphic mapping $f:\mathbb{C}^{m}\rightarrow M$ is said to be a weighted Yosida mapping if for any $z,~ξ\in\mathbb{C}^{m}$ with $\|ξ\|=1,$ the quantity $φ(\|z\|)E_{M}(f(z), df(z)(ξ))$ remains bounded above, where $df(z)$ is the map from $T_z(\mathbb{C}^{m})$ to $T_{f(z)}(M)$ induced by $f.$ We present several criteria of holomorphic mappings belonging to the class of all weighted Yosida mappings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_06800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Yosida Mappings of Several Complex Variables Bharti, Nikhil Van Thin, Nguyen Complex Variables 32A10, 32H02, 32C15, 32H30 Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let $φ: [0,\infty)\rightarrow (0,\infty)$ be positive function such that $$γ_r=\sup\limits_{r\leq a<b}\left|(φ(a)-φ(b))/(a-b)\right|\leq C,~r\in (0,\infty),$$ for some $C\in (0,1],$ and $\lim_{r\rightarrow\infty}γ_r=0.$ A holomorphic mapping $f:\mathbb{C}^{m}\rightarrow M$ is said to be a weighted Yosida mapping if for any $z,~ξ\in\mathbb{C}^{m}$ with $\|ξ\|=1,$ the quantity $φ(\|z\|)E_{M}(f(z), df(z)(ξ))$ remains bounded above, where $df(z)$ is the map from $T_z(\mathbb{C}^{m})$ to $T_{f(z)}(M)$ induced by $f.$ We present several criteria of holomorphic mappings belonging to the class of all weighted Yosida mappings. |
| title | Weighted Yosida Mappings of Several Complex Variables |
| topic | Complex Variables 32A10, 32H02, 32C15, 32H30 |
| url | https://arxiv.org/abs/2408.06800 |