Intrinsic metrics in ring domains

Abstract

<p>Three hyperbolic-type metrics including the triangular ratio metric, the <i>j*</i>-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.<br></p>