Nicola Arcozzi, Daniele Morbidelli
Published 2005-08-24, updated 2008-01-15Version 2
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.
Journal: Comment. Math. Helv. 83 (2008), 101-141
Geodesics in the Heisenberg group $\mathbb{H}^n$ by way of Fourier series
The traveling salesman problem in the Heisenberg group: upper bounding curvature
Weak contact equations for mappings into Heisenberg groups
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