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arXiv · 1911.04807

Duality of moduli in regular metric spaces

Atte Lohvansuu·Kai Rajala
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Abstract

F. Gehring and W. Ziemer proved that the p-modulus of the family of paths connecting two continua is dual to the p^*-modulus of the corresponding family of separating hypersurfaces. In this paper we show that a similar result holds in complete Ahlfors-regular metric spaces that support a weak 1-Poincar\'e inequality. As an application we obtain a new characterization for quasiconformal mappings between such spaces.

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Atte Lohvansuu, Kai Rajala. 2019-11-12. Duality of moduli in regular metric spaces. https://arxiv.org/abs/1911.04807

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