Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds and orbifolds

Abstract

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 manifolds, and complete flat and elliptic 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.

55 pages, preprint

References in corpus (4)

• Structure of measures in Lipschitz differentiability spaces
• An introduction to the Ribe program
• Snowflake universality of Wasserstein spaces
• A Characterization of Bi-Lipschitz Embeddable Metric Spaces in Terms of Local Bi-Lipschitz Embeddability

Cited by in corpus (2)

• Bi-Lipschitz embeddings of $SRA$-free spaces into Euclidean spaces
• Essential minimal volume of Einstein 4-manifolds