| Abstract: |
| One of the local-global themes in the theory of metric embeddings is: suppose that all bounded subsets of an unbounded metric space $A$ admit bilipschitz embeddings into a Banach space $X$ with uniformly bounded distortions. Does the whole metric space $A$ admit a bilipschitz embedding into $X$?
In some cases, we answer this question positively by using smooth transitions between the parts` embeddings; the construction is based on logarithmic spirals. |
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