Infinitesimally small spheres and conformally invariant metrics

Stamatis Pouliasis, Alexander Yu. Solynin

The modulus metric (also called the capacity metric) on a domain $D\subset {\mathbb{R}}^n$ can be defined as $μ_D(x,y)=\inf\{\mbox{cap}\,(D,γ)\}$, where ${\mbox{cap}}\,(D,γ)$ stands…