Several stability theorems concerning biLipschitz maps of the Heisenberg group are established, extending (with nonsharp exponent) analogous results of F. John in Euclidean space. Due to the different geometry, the proof of John can not be extended. A careful analysis of the behavior of geodesics under biLipschitz maps is the main tool of the present paper.
N. Arcozzi, D. Morbidelli (2008). Stability of isometric maps in the Heisenberg group. COMMENTARII MATHEMATICI HELVETICI, 83, 101-141 [10.4171/CMH/120].
Stability of isometric maps in the Heisenberg group
ARCOZZI, NICOLA;MORBIDELLI, DANIELE
2008
Abstract
Several stability theorems concerning biLipschitz maps of the Heisenberg group are established, extending (with nonsharp exponent) analogous results of F. John in Euclidean space. Due to the different geometry, the proof of John can not be extended. A careful analysis of the behavior of geodesics under biLipschitz maps is the main tool of the present paper.File in questo prodotto:
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