Stability of isometric maps in the Heisenberg group

In this paper we prove some approximation results for biLipschitz maps in the Heisenberg group. Namely, we show that a biLipschitz map with biLipschitz constant close to one can be pointwise approximated, quantitatively on any fixed ball, by an isometry. This leds to an approximation in BMO norm for the map's Pansu derivative. We also prove that a global quasigeodesic can be approximated by a geodesic in any fixed segment

The orthogonal projection on slice functions on the quaternionic sphere

We study the $L^p$ norm of the orthogonal projection from the space of quaternion valued $L^2$ functions to the closed subspace of slice $L^2$ functions.Comment: 6 page

From Hankel operators to Carleson measures in a quaternionic variable

We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari anc C. Fefferman are proved.Comment: 19 page