Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds and orbifolds

  title={Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds and orbifolds},
  author={Sylvester David Eriksson-Bique},
We construct bi-Lipschitz embeddings into Euclidean space for manifolds and orbifolds of bounded diameter and curvature.The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. Our results also apply for bounded subsets of complete Riemannian orbifolds. Our approach is based on analysing 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… CONTINUE READING

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