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arXiv · 2105.01309

Intrinsic metrics in ring domains

Oona Rainio
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Abstract

Three hyperbolic type metrics including the triangular ratio metric, the $j^*$-metric and the M\"obius 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 M\"obius-invariant lower bound is proved for the conformal capacity of a general ring domain by using a symmetric quantity defined with the M\"obius metric.

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Oona Rainio. 2021-05-04. Intrinsic metrics in ring domains. https://doi.org/10.1007/s40627-022-00092-5

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