Remarks on conformal modulus in metric spaces - Romney, Matthew (MATHEMATICA SCANDINAVICA, 2023)
We give an example of an Ahlfors 3-regular, linearly locally connected metric space homeomorphic to R^3 containing a nondegenerate continuum E with zero capacity, in the sense that the conformal modulus of the set of nontrivial curves intersecting E is zero. We discuss this example in relation to the quasiconformal uniformization problem for metric spaces.