Abstract
In relation with regularity properties of the transport map in optimal transportation on Riemannian manifolds, convexity of injectivity and nonfocal domains is investigated on the ellipsoid of revolution. Building upon previous results [4, 5], both the oblate and prolate cases are addressed. Preliminary numerical estimates are given in the prolate situation.
The first author is supported by Conseil RĂ©gional de Bourgogne (contract no. 2009-160E-160-CE-160T),ANR Geometric ControlMethods (project no. NT09_504490)and SADCO Initial Training Network (FP7 grant no. 264735-SADCO).
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Notes
- 1.
1 This is not true anymore for conjugate times outside polar or equatorial points; only one axial symmetry is preserved, see Fig. 4.
- 2.
2 apo.enseeiht.fr/cotcot
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Caillau, JB., Royer, C.W. (2014). On the injectivity and nonfocal domains of the ellipsoid of revolution. In: Stefani, G., Boscain, U., Gauthier, JP., Sarychev, A., Sigalotti, M. (eds) Geometric Control Theory and Sub-Riemannian Geometry. Springer INdAM Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-02132-4_5
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