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Smoothness of subRiemannian isometries

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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.

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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  • 10/1/16
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  • 2020-09-21

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