Intrinsic metrics in ring domains - Rainio Oona (Springer International Publishing, 2022)
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.