REMARKS ON CONFORMAL MODULUS IN METRIC SPACES

Matthew Romney

doi:10.7146/math.scand.a-136656

REMARKS ON CONFORMAL MODULUS IN METRIC SPACES

Matthew Romney

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We give an example of an Ahlfors 3-regular, linearly locally connected metric space homeomorphic to R³ 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.

Original language	English
Pages (from-to)	299-310
Number of pages	12
Journal	Mathematica Scandinavica
Volume	129
Issue number	2
DOIs	https://doi.org/10.7146/math.scand.a-136656
State	Published - 2023

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abstract = "We give an example of an Ahlfors 3-regular, linearly locally connected metric space homeomorphic to R3 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.",

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REMARKS ON CONFORMAL MODULUS IN METRIC SPACES

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