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  • Print publication year: 2019
  • Online publication date: October 2019

11 - Regularity of the Sub-Riemannian Distance


In this chapter we investigate the regularity properties of the sub-Riemannian distance from a fixed point. In particular, we prove that the sub-Riemannian distance is smooth on an open and dense subset of every compact ball, but as soon as the distribution is not full dimensional at the point, every level set of the distance contains a nondifferentiability point of the distance itself.