Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target

Details Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target

2006-02-01

arxiv.org/abs/math/0602029v1

Geom. Funct. Anal. 17 (2007), 435-467

Mathematics

Functional Analysis

To appear in Geom. Funct. Anal. (GAFA)

Scientific paper

10.1007/s00039-007-0594-y

We study a question of density of Lipschitz mappings in the Sobolev class of
mappings from a closed manifold into a singular space. The main result of the
paper shows that if we change the metric in the target space to a bi-Lipschitz
equivalent one, than the property of the density of Lipschitz mappings may be
lost.

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