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Shortest paths for sub-Riemannian metrics on rank-two distributions

About this Title

Wensheng Liu and Héctor J. Sussman

Publication: Memoirs of the American Mathematical Society
Publication Year: 1996; Volume 118, Number 564
ISBNs: 978-0-8218-0404-9 (print); 978-1-4704-0143-6 (online)
DOI: https://doi.org/10.1090/memo/0564
MathSciNet review: 1303093
MSC: Primary 53C22; Secondary 49K15, 58E10

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Table of Contents

Chapters

• 1. Introduction
• 2. Three examples
• 3. Notational conventions and definitions
• 4. Abnormal extremals
• 5. Sub-Riemannian manifolds, length minimizers and extremals
• 6. Regular abnormal extremals for rank-two distributions
• 7. Local optimality of regular abnormal extremals
• 8. Strict abnormality
• 9. Some special cases
• Appendix A
• Appendix B
• Appendix C
• Appendix D
• Appendix E