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Sharp distortion growth for bilipschitz extension of planar maps
This note addresses the quantitative aspect of the bilipschitz extension
problem. The main result states that any bilipschitz embedding of
into can be extended to a bilipschitz self-map of
with a linear bound on the distortion.Comment: 9 pages. Slightly expanded introduction, added reference
Lipschitz retraction of finite subsets of Hilbert spaces
Finite subset spaces of a metric space form a nested sequence under
natural isometric embeddings . We prove that
this sequence admits Lipschitz retractions when is a
Hilbert space.Comment: Specializes the result from v1 to Hilbert spaces. The problem remains
open for general Hadamard space
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