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

12 - Abnormal Extremals and Second Variation


This chapter is devoted to the analysis of the second-order conditions for length-minimizers and the analysis of abnormal extremals. After a first result on the regularity of the squared sub-Riemannian distance from a fixed point, showing that Lipschitz regularity is lost at those points reached by only abnormal length-minimizers, we move to second-order conditions, known as the Goh and generalized Legendre conditions.

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