American Journal of Mathematics
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.
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This article appeared in the American Journal of Mathematics, Volume 138, Issue 5, 2016, pages 1439-1454, Copyright © 2016, Johns Hopkins University Press.
Capogna, L. & Le Donne, E. (2016). Smoothness of subRiemannian isometries. American Journal of Mathematics, 138(5), 1439-1454. https://doi.org/10.1353/ajm.2016.0043