Rectifiability and Lipschitz extensions into the Heisenberg group

The Fourier Transforms of Lipschitz Functions on the Heisenberg Group

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the Heisenberg group Hn. We compare our conclusions with some previous results in the field.

1 The Heisenberg group does not admit a bi - Lipschitz embedding into L 1 after

We show that the Heisenberg group, with its Carnot-Caratheodory metric, does not admit a bi-Lipschitz embedding into L1.

LIPSCHITZ ESTIMATES FOR GEODESICS IN THE HEISENBERG GROUP by

Volume Preserving Bi-lipschitz Homeomorphisms on the Heisenberg Group

The use of sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on R lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this m...

Smooth Approximation for Intrinsic Lipschitz Functions in the Heisenberg Group

We characterize intrinsic Lipschitz functions as maps which can be approximated by a sequence of smooth maps, with pointwise convergent intrinsic gradient. We also provide an estimate of the Lipschitz constant of an intrinsic Lipschitz function in terms of the L∞−norm of its intrinsic gradient.