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Smoothness of subRiemannian isometries
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 138, Number 5, October 2016
- pp. 1439-1454
- 10.1353/ajm.2016.0043
- Article
- Additional Information
We show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.