Duality of moduli in regular toroidal metric spaces

We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala [12] on the corresponding duality in condensers. peerReviewed

Symmetriset konveksit kappaleet

On the Modulus Duality in Arbitrary Codimension

Abstract We study the modulus of dual families of $k$- and $(n-k)$-dimensional Lipschitz chains of Euclidean $n$-cubes and establish half of the modulus duality identity.

Quasispheres and metric doubling measures

Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking.