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Smoothness of subRiemannian isometries (1305.5286v2)
Published 22 May 2013 in math.MG, math.AP, and math.DG
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.
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