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MiS Preprint
86/2013

Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces

Piotr Hajlasz and Armin Schikorra

Abstract

We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz mappings Lip(X,Y) are dense in N^{1,p}(X,Y) whenever the Nagata dimension of X is bounded by n and the space X supports the p-Poincare inequality.

Received:
Aug 16, 2013
Published:
Aug 16, 2013
MSC Codes:
46E35, 55Q70

Related publications

inJournal
2014 Journal Open Access
Piotr Hajlasz and Armin Schikorra

Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces

In: Annales Academiae Scientiarum Fennicae / Mathematica, 39 (2014) 2, pp. 593-604