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

Abstract

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.

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

Cited by in corpus (2)

• Monotone Sobolev Mappings of planar domains and surfaces
• On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target