Stability of isometric maps in the Heisenberg group

Details Stability of isometric maps in the Heisenberg group Stability of isometric maps in the Heisenberg group

2005-08-24

arxiv.org/abs/math/0508474v2

Comment. Math. Helv. 83 (2008), 101-141

Mathematics

Metric Geometry

Scientific paper

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.

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