Duality of moduli in regular toroidal metric spaces

TL;DR

This paper extends the duality principles of moduli and capacities from solid tori to a broader class of regular metric spaces, advancing the understanding of geometric analysis in these contexts.

Contribution

It generalizes the duality of moduli and capacities from specific solid tori to a wider class of regular metric spaces, building on previous work on condensers.

Findings

Established duality in regular metric spaces

Extended previous results from solid tori to general spaces

Contributed to the theory of geometric analysis in metric spaces

Abstract

We generalize a result of Freedman and He, 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 K. Rajala on the corresponding duality in condensers.