Rectifiability and Lipschitz extensions into the Heisenberg group

Denote by $${\mathbb{H}^n}$$ the 2n+1 dimensional Heisenberg group. We show that the pairs $${(\mathbb{R}^k ,\mathbb{H}^n)}$$ and $${(\mathbb{H}^k ,\mathbb{H}^n)}$$ do not have the Lipschitz extension property for k >