Spaces of differential forms and maps with controlled distortion

摘要

We study necessary and sufficient conditions for an approximately differentiable map f: M → M' between Riemannian manifolds to induce a bounded transfer operator of differential forms with respect to the norms of Lebesgue spaces. As a corollary, we see that every homeomorphism f: M → M' of class ACL(M) whose transfer operator of differential forms with norm in λ_p is an isomorphism must necessarily be either quasiconformal or quasi-isometric. We give some applications of our results to the study of the functoriality of cohomology in Lebesgue spaces.