2017/06/17 by Manzi Huang, Antti Rasila, Huang, Manzi +5
Engineering · Mathematics · #30F45 #30L10 #Analytic and geometric function theory #Bounded function #Characterization (materials science) #Combinatorics #Complex Variables (math.CV) #Computer science #Engineering #Euclidean distance #Euclidean geometry #Euclidean space #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Mathematical analysis #Mathematics #Metric (unit) #Metric space #Optics #Physics #Primary: 30C65 #Pure mathematics #Secondary: 30C20 #Space (punctuation)
paper · pdf · doi:10.48550/arxiv.1706.05494
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2017/06/17 · openalex created_date 2017/06/30 · openalex updated_date 2026/08/05
In this paper, we study the characterization of inner uniformity of bounded domains G in \IRn, and prove that the following three conditions are equivalent: (1) G is inner uniform; (2) G is Gromov hyperbolic and its inner metric boundary is naturally quasisymmetrically equivalent to the Gromov boundary; (3) G is Gromov hyperbolic and linearly locally connected with respect to the inner metric. The equivalence between the conditions (1) and (2), and the implication from (2) to (3) affirmatively answer three questions raised by Bonk, Heinonen, and Koskela in 2001.