# Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard Bonnard; Jean-Baptiste Caillau; Gabriel Janin

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 2, page 533-554
- ISSN: 1292-8119

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topBonnard, Bernard, Caillau, Jean-Baptiste, and Janin, Gabriel. "Conjugate-cut loci and injectivity domains on two-spheres of revolution." ESAIM: Control, Optimisation and Calculus of Variations 19.2 (2013): 533-554. <http://eudml.org/doc/272950>.

@article{Bonnard2013,

abstract = {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.},

author = {Bonnard, Bernard, Caillau, Jean-Baptiste, Janin, Gabriel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {conjugate and cut loci; injectivity domain; optimal control; optimal transport},

language = {eng},

number = {2},

pages = {533-554},

publisher = {EDP-Sciences},

title = {Conjugate-cut loci and injectivity domains on two-spheres of revolution},

url = {http://eudml.org/doc/272950},

volume = {19},

year = {2013},

}

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

PB - EDP-Sciences

VL - 19

IS - 2

SP - 533

EP - 554

AB - 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.

LA - eng

KW - conjugate and cut loci; injectivity domain; optimal control; optimal transport

UR - http://eudml.org/doc/272950

ER -

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