Remarks on conformal modulus in metric spaces

2022/08/25 by Matthew Romney, Romney, Matthew
Computer Science · Mathematics · #30L10 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #Metric Geometry (math.MG) #math.CV #math.MG #msc:30L10

paper · pdf · doi:10.48550/arxiv.2208.12132

8 pages, 1 figure

arxiv created 2022/08/25 · openalex publication_date 2022/08/25 · arxiv updated 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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