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Planar bilipschitz extension from separated nets
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DOI：10.1112/jlms.70540.png)
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Abstract
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We prove that every -bilipschitz mapping can be extended to a -bilipschitz mapping , and we provide a polynomial upper bound for . Moreover, we extend the result to every separated net in instead of , with the upper bound gaining a polynomial dependence on the separation and net constants associated to the given separated net. This answers an Oberwolfach question of Navas from 2015 and is also a positive solution of the two-dimensional form of a decades old open (in all dimensions at least two) problem due to Alestalo Trotsenko and V & auml;is & auml;l & auml;.
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