A New Metric Associated with the Domain Boundary A New Metric Associated with the Domain Boundary

In this paper, we introduce a new metric c ~ which is associated with the domain boundary for a Ptolemy space ( X ,  d ). Moreover, we study inclusion relations of c ~ metric balls and some related hyperbolic type metric balls in subdomains of R n . In addition, we study distortion properties of the...

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Bibliographic Details
Published in:Computational methods and function theory Vol. 25; no. 4; pp. 765 - 784
Main Authors: Song, Xingchen, Wang, Gendi
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2025
Springer Nature B.V
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Geometric transformation
Inequality
Mathematics
Mathematics and Statistics
Möbius transformation
metric
Metric ball
Quasiconformality
Ball inclusion
30F45 (51E05)
ISSN:1617-9447, 2195-3724
Online Access:Get full text
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Summary:In this paper, we introduce a new metric c ~ which is associated with the domain boundary for a Ptolemy space ( X ,  d ). Moreover, we study inclusion relations of c ~ metric balls and some related hyperbolic type metric balls in subdomains of R n . In addition, we study distortion properties of the c ~ metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the c ~ metric.
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-024-00545-4