Curvature: A Variational Approach

ISBN-13: 9781470426460 / Angielski / Miękka / 2018 / 116 str.

A. Agrachev;D. Barilari;L. Rizzi

Spis treści

• Introduction
• Part 1. Statements of the results: General setting
• Flag and growth vector of an admissible curve
• Geodesic cost and its asymptotics
• Sub-Riemannian geometry
• Part 2. Technical tools and proofs: Jacobi curves
• Asymptotics of the Jacobi curve: equiregular case
• Sub-Laplacian and Jacobi curves
• Part 3. Appendix: Appendix A. Smoothness of value function (Theorem $2.19$)
• Appendix B. Convergence of approximating Hamiltonian systems (Proposition 5.15)
• Appendix C. Invariance of geodesic growth vector by dilations (Lemma $5.20$)
• Appendix D. Regularity of $C(t,s)$ for the Heisenberg group (Proposition $5.51$)
• Appendix E. Basics on curves in Grassmannians (Lemma $3.5$ and $6.5$)
• Appendix F. Normal conditions for the canonical frame
• Appendix G. Coordinate representation of flat, rank 1 Jacobi curves (Proposition $7.7$)
• Appendix H. A binomial identity (Lemma $7.8$)
• Appendix I. A geometrical interpretation of $\dot c_t$
• Bibliography
• Index.