Schwarz–Pick Estimates of the Real Unit Ball for Harmonic Mappings

In this paper, Schwarz–Pick estimates are obtained for harmonic mappings from the unit ball of ℝ n into origin-symmetric bounded convex domains Ω ⊂ ℝ m , which extends the recent results of Liu [ 7 ], Chen and Hamada [ 2 ]. This approach is new and functional, which is based on some geometric proper...

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Bibliographic Details
Published in:Frontiers of Mathematics 2024-03, Vol.19 (2), p.283-294
Main Authors: Wang, Jianfei, Liu, Taishun, Hu, Chunying
Format: Article
Language:English
Subjects:
Convexity
Estimates
Mapping
Mathematics
Mathematics and Statistics
Research Article
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Summary:In this paper, Schwarz–Pick estimates are obtained for harmonic mappings from the unit ball of ℝ n into origin-symmetric bounded convex domains Ω ⊂ ℝ m , which extends the recent results of Liu [ 7 ], Chen and Hamada [ 2 ]. This approach is new and functional, which is based on some geometric properties of convex domains; and the domains discussed are rather general. Notice that when Ω is the unit p -ball in ℝ m , our main theorem reduces to that of Chen and Hamada [ 2 ].
ISSN:2731-8648
1673-3452
2731-8656
1673-3576
DOI:10.1007/s11464-022-0058-6