Abstract:The modulus metric (also called the capacity metric) on a domain D ⊂ R n can be defined as µ D (x, y) = inf{cap (D, γ)}, where cap (D, γ) stands for the capacity of the condenser (D, γ) and the infimum is taken over all continua γ ⊂ D containing the points x and y. It was conjectured by J. Ferrand, G. Martin and M. Vuorinen in 1991 that every isometry in the modulus metric is a conformal mapping. In this note, we confirm this conjecture and prove new geometric properties of surfaces that are spheres in the met… Show more
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