Intrinsic metrics in ring domains

Three hyperbolic-type metrics including the triangular ratio metric, the j ∗ -metric, and the Möbius metric are studied in an annular ring. The Euclidean midpoint rotation is introduced as a method to create upper and lower bounds for these metrics, and their sharp inequalities are found. A new Möbi...

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Bibliographic Details
Published in:Complex analysis and its synergies 2022-03, Vol.8 (1), Article 3
Main Author: Rainio, Oona
Format: Article
Language:English
Subjects:
Algebraic Geometry
Analysis
Domains
Dynamical Systems and Ergodic Theory
Functional Analysis
Functions of a Complex Variable
Lower bounds
Mathematics
Mathematics and Statistics
Partial Differential Equations
Rings (mathematics)
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Summary:Three hyperbolic-type metrics including the triangular ratio metric, the j ∗ -metric, and the Möbius metric are studied in an annular ring. The Euclidean midpoint rotation is introduced as a method to create upper and lower bounds for these metrics, and their sharp inequalities are found. A new Möbius-invariant lower bound is proved for the conformal capacity of a general ring domain by using a symmetric quantity defined with the Möbius metric.
ISSN:2524-7581
2197-120X
DOI:10.1007/s40627-022-00092-5