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arXiv · 2102.03035

On the Sharp Lower Bound for Duality of Modulus

Sylvester Eriksson-Bique·Pietro Poggi-Corradini
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Abstract

We establish a sharp reciprocity inequality for modulus in compact metric spaces $X$ with finite Hausdorff measure. In particular, when $X$ is also homeomorphic to a planar rectangle, our result answers a question of K. Rajala and M. Romney. More specifically, we obtain a sharp inequality between the modulus of the family of curves connecting two disjoint continua $E$ and $F$ in $X$ and the modulus of the family of surfaces of finite Hausdorff measure that separate $E$ and $F$. The paper also develops approximation techniques, which may be of independent interest.

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BibTeXRIS

Sylvester Eriksson-Bique, Pietro Poggi-Corradini. 2021-02-05. On the Sharp Lower Bound for Duality of Modulus. https://arxiv.org/abs/2102.03035

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