Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions

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Introduction
Three examples Notational conventions and definitions
Abnormal extremals Sub-Riemannian manifolds, length minimizers and extremals
Regular abnormal extremals for rank-two distributions
Local optimality of regular abnormal extremals
Strict abnormality Some special cases
The Gaveau-Brockett problem
Proof of Theorem 1
Local optimality of normal extremals
Rigid sub-Riemannian arcs and local optimality
A nonoptimality proof
References
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