Bi-Lipschitz embeddings revisited

2025/01/13 by Movahedi-Lankarani, H., Wells, R.
#FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2501.07648

Abstract

Given a metric space (X, d), we continue our study of the distance function x↦ d(x,-) and its relation to bi-Lipschitz embeddings of (X, d) into R^N. As application, given a compact metric-measure space (X, d,μ), we give three sufficient conditions for the existence of such a bi-Lipschitz embedding.

Related

• A Characterization of Bi-Lipschitz Embeddable Metric Spaces in Terms of Local Bi-Lipschitz Embeddability
• Lipschitz Embeddings of Metric Spaces into c₀
• Bi-Lipschitz embeddings of the space of unordered m-tuples with a partial transportation metric
• Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space
• Bi-Lipschitz arcs in metric spaces with controlled geometry