Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces

Piotr Hajlasz; Armin Schikorra

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arXiv · 1306.6502

Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces

Piotr Hajlasz·Armin Schikorra

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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.

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BibTeX RIS

Piotr Hajlasz, Armin Schikorra. 2013-06-27. Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces. https://arxiv.org/abs/1306.6502

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