Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds and orbifolds
نویسنده
چکیده
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 Rn/Γ , where Γ is a discrete group acting properly discontinuously and by isometries on Rn . 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.
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