Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
Geometric Topology
2013-06-28 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1306.6502,
title = {Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces},
author = {Piotr Hajlasz and Armin Schikorra},
journal= {arXiv preprint arXiv:1306.6502},
year = {2013}
}