Smoothness of Subriemannian Isometries

Authors

Luca Capogna, University of Minnesota Twin CitiesFollow
Enrico Le Donne, University of Jyväskylä

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

1439

Last Page

1454

DOI

10.1353/ajm.2016.0043

ISSN

00029327

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Capogna, Luca and Le Donne, Enrico, "Smoothness of Subriemannian Isometries" (2016). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/128