In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 1081-1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is g = dϕ2 + m(ϕ)dθ2 to the period mapping of the ϕ-variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the convexity properties of the injectivity domains of such metrics. These properties have applications in optimal control of space and quantum mechanics, and in optimal transport.
Mots-clés : conjugate and cut loci, injectivity domain, optimal control, optimal transport
@article{COCV_2013__19_2_533_0,
author = {Bonnard, Bernard and Caillau, Jean-Baptiste and Janin, Gabriel},
title = {Conjugate-cut loci and injectivity domains on two-spheres of revolution},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {533--554},
publisher = {EDP-Sciences},
volume = {19},
number = {2},
year = {2013},
doi = {10.1051/cocv/2012020},
mrnumber = {3049722},
zbl = {1267.53042},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2012020/}
}
TY - JOUR AU - Bonnard, Bernard AU - Caillau, Jean-Baptiste AU - Janin, Gabriel TI - Conjugate-cut loci and injectivity domains on two-spheres of revolution JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 533 EP - 554 VL - 19 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012020/ DO - 10.1051/cocv/2012020 LA - en ID - COCV_2013__19_2_533_0 ER -
%0 Journal Article %A Bonnard, Bernard %A Caillau, Jean-Baptiste %A Janin, Gabriel %T Conjugate-cut loci and injectivity domains on two-spheres of revolution %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 533-554 %V 19 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012020/ %R 10.1051/cocv/2012020 %G en %F COCV_2013__19_2_533_0
Bonnard, Bernard; Caillau, Jean-Baptiste; Janin, Gabriel. Conjugate-cut loci and injectivity domains on two-spheres of revolution. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 533-554. doi : 10.1051/cocv/2012020. http://www.numdam.org/articles/10.1051/cocv/2012020/
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