Abstract
We prove that in the Heisenberg group the image of a uniform domain under a global quasiconformal homeomorphism is still a uniform domain. As a consequence, the class of NTA (non-tangentially accessible) domains in the Heisenberg group is also quasiconformally invariant. A large class of non-differentiable Lipschitz quasiconformal homeomorphisms is constructed. The images of smooth domains under these rough mappings give a class of non-smooth NTA domains in the Heisenberg group.
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