2015/07/31 by Sylvester Eriksson‐Bique, Sylvester Eriksson-Bique · 5 citations
Mathematics · #Bounded function #Curvature #Dimension (graph theory) #Embedding #Euclidean space #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Hyperbolic space #Lipschitz continuity #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Point processes and geometric inequalities #Pure mathematics #Ricci curvature #Ricci-flat manifold #Riemannian manifold #Scalar curvature #Sectional curvature #Space (punctuation) #math.DG #math.MG #msc:20H15 #msc:30L05 #msc:51F99 #msc:53B20 #msc:53C21
paper · pdf · doi:10.2140/gt.2018.22.1961
published in Geometry & Topology 22(4), 1961-2026 (Mathematical Sciences Publishers) · 55 pages, preprint
arxiv created 2017/04/12 · openalex publication_date 2018/04/05 · arxiv updated 2018/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct bi-Lipschitz embeddings into Euclidean space for bounded-diameter subsets of manifolds and orbifolds of bounded curvature. The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. We also construct global bi-Lipschitz embeddings for spaces of the form [math] , where [math] is a discrete group acting properly discontinuously and by isometries on [math] . This generalizes results of Naor and Khot. Our approach is based on analyzing the structure of a bounded-curvature manifold at various scales by specializing methods from collapsing theory to a certain class of model spaces. In the process, we develop tools to prove collapsing theory results using algebraic techniques.