2019/09/23 by Joshua C. Kline, Kline, Joshua, Jeff Lindquist +3
Mathematics · #30L10 #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1909.10619
openalex publication_date 2019/09/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We prove a Carath 'eodory-type extension of BQS homeomorphisms between two\ndomains in proper, locally path-connected metric spaces as homeomorphisms\nbetween their prime end closures. We also give a Carath 'eodory-type extension\nof geometric quasiconformal mappings between two such domains provided the two\ndomains are both Ahlfors Q-regular and support a Q-Poincar 'e inequality\nwhen equipped with their respective Mazurkiewicz metrics. We also provide\nexamples to demonstrate the strengths and weaknesses of prime end closures in\nthis context.\n