Calculus of Variations and Geometric Measure Theory
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L. Capogna - E. Le Donne

Smoothness of subRiemannian isometries

created by ledonne on 21 Dec 2018



Inserted: 21 dec 2018

Year: 2013

ArXiv: 1305.5286 PDF


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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