Higher degree obstructions to quasiconformal equivalence
arXiv:2607.11331
summary
The paper demonstrates that certain diffeomorphic Riemannian manifolds cannot be related by quasiconformal maps, using a degree‑2 conformal cohomology obstruction, and provides analogous examples in the contact sub‑Riemannian setting.
Abstract
Pairs of diffeomorphic Riemannian manifolds are shown not to be quasiconformally equivalent, while no degree one invariant (extremal lengths, conformal parabolicity,...) can distinguish them. The obstruction arises from conformal cohomology in degree 2. Similar examples are constructed in the contact subRiemannian category
Topics & keywords
#quasiconformal maps#riemannian manifolds#conformal cohomology#metric geometry#subriemannian geometrydegree 2 conformal cohomologyquasiconformal equivalencediffeomorphic manifoldscontact subriemannianextremal length