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

Abstract

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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.

How to cite

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Bonnard, 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 -

References

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