Document Type

Article

Publication Date

10-1-2016

Publication Title

American Journal of Mathematics

Abstract

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.

Volume

138

Issue

5

First Page Number

1439

Last Page Number

1454

DOI

10.1353/ajm.2016.0043

Version

Preprint

Publisher Statement

This article appeared in the American Journal of Mathematics, Volume 138, Issue 5, 2016, pages 1439-1454, Copyright © 2016, Johns Hopkins University Press.

Rights

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.

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