[Convexité des domaines d'injectivité sur l'ellipsoïde de révolution : le cas oblate]
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.
Accepté le :
Publié le :
Bernard Bonnard 1 ; Jean-Baptiste Caillau 1 ; Ludovic Rifford 2
@article{CRMATH_2010__348_23-24_1315_0,
author = {Bernard Bonnard and Jean-Baptiste Caillau and Ludovic Rifford},
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},
number = {23-24},
year = {2010},
doi = {10.1016/j.crma.2010.10.036},
language = {en},
}
TY - JOUR AU - Bernard Bonnard AU - Jean-Baptiste Caillau AU - Ludovic Rifford TI - Convexity of injectivity domains on the ellipsoid of revolution: The oblate case JO - Comptes Rendus. Mathématique PY - 2010 SP - 1315 EP - 1318 VL - 348 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2010.10.036 LA - en ID - CRMATH_2010__348_23-24_1315_0 ER -
%0 Journal Article %A Bernard Bonnard %A Jean-Baptiste Caillau %A Ludovic Rifford %T Convexity of injectivity domains on the ellipsoid of revolution: The oblate case %J Comptes Rendus. Mathématique %D 2010 %P 1315-1318 %V 348 %N 23-24 %I Elsevier %R 10.1016/j.crma.2010.10.036 %G en %F CRMATH_2010__348_23-24_1315_0
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] Géodésiques des surfaces de révolution, Semin. Théor. Spectr. Geom., Volume S9 (1991), pp. 33-38
[2] 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] 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] Geodesics and deformed spheres, Proc. Amer. Math. Soc., Volume 100 (1987) no. 3, pp. 522-525
[6] Continuity of optimal transport maps and convexity of injectivity domains on small deformations of , Comm. Pure Appl. Math., Volume 62 (2009) no. 12, pp. 1670-1706
[7] 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] 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] Traité des fonctions elliptiques et de leurs applications, Première Partie, Gauthier-Villars, 1886
[12] , Optimal Transport, Old and New, vol. 338, Springer, 2009
Cité par Sources :
Commentaires - Politique