Comptes Rendus
no. 23-24
Differential Geometry
Convexity of injectivity domains on the ellipsoid of revolution: The oblate case
[Convexité des domaines d'injectivité sur l'ellipsoïde de révolution : le cas oblate]

Présenté par : Gilles Lebeau

Bernard Bonnard1 ; Jean-Baptiste Caillau1 ; Ludovic Rifford2
1 Institut de Mathématiques, Université de Bourgogne & CNRS, 9, avenue Savary, 21078 Dijon, France
2 Laboratoire J.A. Dieudonné, Université de Nice & CNRS, parc Valrose, 06108 Nice, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1315-1318.

On caractérise les propriétés de convexité du domaine d'injectivité sur un ellipsoïde de révolution oblate.

We characterize the convexity properties of the tangent injectivity domain on an the ellipsoid of revolution in the oblate case.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.036
Bernard Bonnard 1 ; Jean-Baptiste Caillau 1 ; Ludovic Rifford 2

1 Institut de Mathématiques, Université de Bourgogne & CNRS, 9, avenue Savary, 21078 Dijon, France
2 Laboratoire J.A. Dieudonné, Université de Nice & CNRS, parc Valrose, 06108 Nice, France 
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     title = {Convexity of injectivity domains on the ellipsoid of revolution: {The} oblate case},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1315--1318},
     publisher = {Elsevier},
     volume = {348},
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     year = {2010},
     doi = {10.1016/j.crma.2010.10.036},
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Bernard Bonnard; Jean-Baptiste Caillau; Ludovic Rifford. Convexity of injectivity domains on the ellipsoid of revolution: The oblate case. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1315-1318. doi : 10.1016/j.crma.2010.10.036. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.036/

[1] G. Besson Géodésiques des surfaces de révolution, Semin. Théor. Spectr. Geom., Volume S9 (1991), pp. 33-38

[2] B. Bonnard; J.-B. Caillau Optimality results in orbit transfer, C. R. Acad. Sci. Paris, Ser. I, Volume 345 (2007), pp. 319-324

[3] B. Bonnard, J.-B. Caillau, Singular metrics on the two-sphere in space mechanics, HAL preprint, 2008, no. 00319299, 1–25.

[4] B. Bonnard; J.-B. Caillau; R. Sinclair; M. Tanaka Conjugate and cut loci of a two-sphere of revolution with application to optimal control, Ann. Inst. H. Poincare Anal. Non Lineaire, Volume 26 (2009) no. 4, pp. 1081-1098

[5] A.M. Faridi; E.L. Schucking Geodesics and deformed spheres, Proc. Amer. Math. Soc., Volume 100 (1987) no. 3, pp. 522-525

[6] A. Figalli; L. Rifford Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S2, Comm. Pure Appl. Math., Volume 62 (2009) no. 12, pp. 1670-1706

[7] A. Figalli; L. Rifford; C. Villani On the Ma–Trudinger–Wang curvature on surfaces, Calc. Var. Partial Differential Equations, Volume 39 (2010) no. 3–4, pp. 307-332

[8] A. Figalli, L. Rifford, C. Villani, Nearly round spheres look convex, Preprint, 2010.

[9] A. Figalli, L. Rifford, C. Villani, Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds, preprint, 2010.

[10] R. Sinclair; M. Tanaka The cut locus of a two-sphere of revolution and Topogonov's comparison theorem, Tohoku Math. J., Volume 59 (2007) no. 2, pp. 379-399

[11] G.-H. Halphen Traité des fonctions elliptiques et de leurs applications, Première Partie, Gauthier-Villars, 1886

[12] C. Villani, Optimal Transport, Old and New, vol. 338, Springer, 2009

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