2018/06/07 by Angela Y. Wu, Wu, Angela
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1806.02917
openalex publication_date 2018/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for all n ≥ 2, there exists a doubling linearly locally contractible metric space X that is topologically a n-sphere such that every weak tangent is isometric to \Rn but X is not quasisymmetrically equivalent to the standard n-sphere. The same example shows that 2-Ahlfors regularity in Theorem 1.1 of \citeBK02 on quasisymmetric uniformization of metric 2-spheres is optimal.