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Preface
Un-reduction
1. | Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom, United Kingdom |
2. | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom |
3. | Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure de Paris, 75005 Paris, France |
References:
[1] |
M. Bauer, P. Harms and P. W. Michor, Almost local metrics on shape space of hypersurfaces in n-space,, to appear in: SIAM Journal on Imaging Sciences, (). Google Scholar |
[2] |
A. Clark, C. Cotter and J. Peiro, A reparameterisation-based approach to geodesic shooting for 2D curve matching,, work in progress., (). Google Scholar |
[3] |
H. Cendra, D. D. Holm, J. E. Marsden and T. S. Ratiu, Lagrangian reduction, the Euler-Poincaré equations, and semidirect products,, in, 186 (1998), 1.
|
[4] |
H. Cendra, J. E. Marsden and T. S. Ratiu, Lagrangian reduction by stages,, Mem. Amer. Math. Soc., 152 (2001).
|
[5] |
C. J. Cotter, The variational particle-mesh method for matching curves,, J. Phys. A, 41 (2008).
|
[6] |
C. J. Cotter and D. D. Holm, Geodesic boundary value problems with symmetry,, J. Geom. Mech., 2 (2010), 51.
|
[7] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm, V. Putkaradze and T. S. Ratiu, Symmetry reduced dynamics of charged molecular strands,, Arch. Rational Mech. Anal., 197 (2010), 811.
doi: 10.1007/s00205-010-0305-y. |
[8] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm and T. S. Ratiu, Lagrange-Poincaré field equations,, J. Geom. Phys., 61 (2011), 2120.
|
[9] |
F. Gay-Balmaz, D. D. Holm, D. M. Meier, T. S. Ratiu and F.-X. Vialard, Invariant higher-order variational problems,, Comm. Math. Phys. \textbf{309}(2), 309 (): 413. Google Scholar |
[10] |
F. Gay-Balmaz, D. D. Holm and T. S. Ratiu, Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions, Journal of the Brazilian mathematical society, 42 (): 579. Google Scholar |
[11] |
D. D. Holm, J. E. Marsden and T. S. Ratiu, The Euler-Poincaré equations and semidirect products with applications to continuum theories,, Adv. Math., 137 (1998), 1.
doi: 10.1006/aima.1998.1721. |
[12] |
A. Kriegl and P. W. Michor, "The Convenient Setting of Global Analysis,", Mathematical Surveys and Monographs, 53 (1997).
|
[13] |
J. E. Marsden, "Lectures on Mechanics,", London Mathematical Society Lecture Note Series, 174 (1992).
|
[14] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry. A Basic Exposition of Classical Mechanical Systems," Texts in Applied Mathematics, 17,, Springer-Verlag, (1994).
|
[15] |
P. W. Michor, Manifolds of smooth maps. III: The principal bundle of embeddings of a noncompact smooth manifold,, Cah. Top. Géom. Diff., 21 (1980), 325.
|
[16] |
P. W. Michor and D. Mumford, An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach,, Appl. Comput. Harmon. Anal., 23 (2007), 74.
doi: 10.1016/j.acha.2006.07.004. |
[17] |
P. W. Michor and D. Mumford, Riemannian geometries on spaces of plane curves,, J. Eur. Math. Soc., 8 (2006), 1.
doi: 10.4171/JEMS/37. |
[18] |
R. Montgomery, Gauge theory of the falling cat,, in, 1 (1993), 193.
|
[19] |
F.-X. Vialard, "Hamiltonian Approach to Shape Spaces in a Diffeomorphic Framework: From the Discontinuous Image Matching Problem to a Stochastic Growth Model,", Ph.D Thesis, (2009). Google Scholar |
[20] |
L. Younes, "Shapes and Diffeomorphisms,", Applied Mathematical Sciences, 171 (2010).
|
[21] |
L. Younes, F. Arrate and M. I. Miller, Evolutions equations in computational anatomy,, NeuroImage, 45 (2009).
doi: 10.1016/j.neuroimage.2008.10.050. |
show all references
References:
[1] |
M. Bauer, P. Harms and P. W. Michor, Almost local metrics on shape space of hypersurfaces in n-space,, to appear in: SIAM Journal on Imaging Sciences, (). Google Scholar |
[2] |
A. Clark, C. Cotter and J. Peiro, A reparameterisation-based approach to geodesic shooting for 2D curve matching,, work in progress., (). Google Scholar |
[3] |
H. Cendra, D. D. Holm, J. E. Marsden and T. S. Ratiu, Lagrangian reduction, the Euler-Poincaré equations, and semidirect products,, in, 186 (1998), 1.
|
[4] |
H. Cendra, J. E. Marsden and T. S. Ratiu, Lagrangian reduction by stages,, Mem. Amer. Math. Soc., 152 (2001).
|
[5] |
C. J. Cotter, The variational particle-mesh method for matching curves,, J. Phys. A, 41 (2008).
|
[6] |
C. J. Cotter and D. D. Holm, Geodesic boundary value problems with symmetry,, J. Geom. Mech., 2 (2010), 51.
|
[7] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm, V. Putkaradze and T. S. Ratiu, Symmetry reduced dynamics of charged molecular strands,, Arch. Rational Mech. Anal., 197 (2010), 811.
doi: 10.1007/s00205-010-0305-y. |
[8] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm and T. S. Ratiu, Lagrange-Poincaré field equations,, J. Geom. Phys., 61 (2011), 2120.
|
[9] |
F. Gay-Balmaz, D. D. Holm, D. M. Meier, T. S. Ratiu and F.-X. Vialard, Invariant higher-order variational problems,, Comm. Math. Phys. \textbf{309}(2), 309 (): 413. Google Scholar |
[10] |
F. Gay-Balmaz, D. D. Holm and T. S. Ratiu, Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions, Journal of the Brazilian mathematical society, 42 (): 579. Google Scholar |
[11] |
D. D. Holm, J. E. Marsden and T. S. Ratiu, The Euler-Poincaré equations and semidirect products with applications to continuum theories,, Adv. Math., 137 (1998), 1.
doi: 10.1006/aima.1998.1721. |
[12] |
A. Kriegl and P. W. Michor, "The Convenient Setting of Global Analysis,", Mathematical Surveys and Monographs, 53 (1997).
|
[13] |
J. E. Marsden, "Lectures on Mechanics,", London Mathematical Society Lecture Note Series, 174 (1992).
|
[14] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry. A Basic Exposition of Classical Mechanical Systems," Texts in Applied Mathematics, 17,, Springer-Verlag, (1994).
|
[15] |
P. W. Michor, Manifolds of smooth maps. III: The principal bundle of embeddings of a noncompact smooth manifold,, Cah. Top. Géom. Diff., 21 (1980), 325.
|
[16] |
P. W. Michor and D. Mumford, An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach,, Appl. Comput. Harmon. Anal., 23 (2007), 74.
doi: 10.1016/j.acha.2006.07.004. |
[17] |
P. W. Michor and D. Mumford, Riemannian geometries on spaces of plane curves,, J. Eur. Math. Soc., 8 (2006), 1.
doi: 10.4171/JEMS/37. |
[18] |
R. Montgomery, Gauge theory of the falling cat,, in, 1 (1993), 193.
|
[19] |
F.-X. Vialard, "Hamiltonian Approach to Shape Spaces in a Diffeomorphic Framework: From the Discontinuous Image Matching Problem to a Stochastic Growth Model,", Ph.D Thesis, (2009). Google Scholar |
[20] |
L. Younes, "Shapes and Diffeomorphisms,", Applied Mathematical Sciences, 171 (2010).
|
[21] |
L. Younes, F. Arrate and M. I. Miller, Evolutions equations in computational anatomy,, NeuroImage, 45 (2009).
doi: 10.1016/j.neuroimage.2008.10.050. |
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