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Volumn 16, Issue 4, 2017, Pages 745-785

SUB-RIEMANNIAN STRUCTURES ON GROUPS OF DIFFEOMORPHISMS

Author keywords

abnormal geodesics; group of diffeomorphisms; Moser theorems; normal geodesics; reachability; sub Riemannian geometry

Indexed keywords


EID: 84938840042     PISSN: 14747480     EISSN: 14753030     Source Type: Journal    
DOI: 10.1017/S1474748015000249     Document Type: Article
Times cited : (13)

References (46)
  • 1
    • 72649090470 scopus 로고    scopus 로고
    • Any sub-Riemannian metric has points of smoothness
    • A. A. Agrachev, Any sub-Riemannian metric has points of smoothness, Russian Math. Dokl. 79 (2009), 1-3.
    • (2009) Russian Math. Dokl. , vol.79 , pp. 1-3
    • Agrachev, A.A.1
  • 4
    • 7544243351 scopus 로고    scopus 로고
    • Transport equation and Cauchy problem for BV vector fields
    • L. Ambrosio, Transport equation and Cauchy problem for BV vector fields, Invent. Math. 158(2) (2004), 227-260.
    • (2004) Invent. Math. , vol.158 , Issue.2 , pp. 227-260
    • Ambrosio, L.1
  • 5
    • 84930087131 scopus 로고    scopus 로고
    • Shape deformation analysis from the optimal control viewpoint
    • S. Arguillère, E. Trélat, A. Trouvé and and L. Younes, Shape deformation analysis from the optimal control viewpoint, J. Math. Pures Appl. 104 (2015), 139-178.
    • (2015) J. Math. Pures Appl. , vol.104 , pp. 139-178
    • Arguillère, S.1    Trélat, E.2    Trouvé, A.3    Younes, L.4
  • 6
    • 0001356905 scopus 로고
    • Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des uides parfaits
    • V. Arnol'd, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des uides parfaits, Ann. Inst. Fourier (Grenoble) 16(1) (1966), 319-361.
    • (1966) Ann. Inst. Fourier (Grenoble) , vol.16 , Issue.1 , pp. 319-361
    • Arnol'D, V.1
  • 7
    • 84878114701 scopus 로고    scopus 로고
    • Geodesic distance for right invariant sobolev metrics of fractional order on the diffeomorphism group
    • M. Bauer, M. Bruveris, P. Harms and P. W. Michor, Geodesic distance for right invariant sobolev metrics of fractional order on the diffeomorphism group, Ann. Global Anal. Geom. 44(1) (2013), 5-21.
    • (2013) Ann. Global Anal. Geom. , vol.44 , Issue.1 , pp. 5-21
    • Bauer, M.1    Bruveris, M.2    Harms, P.3    Michor, P.W.4
  • 8
    • 85027954552 scopus 로고    scopus 로고
    • Overview of the geometries of shape spaces and diffeomorphism groups
    • M. Bauer, M. Bruveris and P. W. Michor, Overview of the geometries of shape spaces and diffeomorphism groups, J. Math. Imaging Vision 50 (2014), 60-97.
    • (2014) J. Math. Imaging Vision , vol.50 , pp. 60-97
    • Bauer, M.1    Bruveris, M.2    Michor, P.W.3
  • 9
    • 84879998697 scopus 로고    scopus 로고
    • Sobolev metrics on the manifold of all Riemannian metrics
    • M. Bauer, P. Harms and P. W. Michor, Sobolev metrics on the manifold of all Riemannian metrics, J. Differential Geom. 94(2) (2013), 187-208.
    • (2013) J. Differential Geom. , vol.94 , Issue.2 , pp. 187-208
    • Bauer, M.1    Harms, P.2    Michor, P.W.3
  • 10
    • 84865294684 scopus 로고    scopus 로고
    • Sobolev metrics on shape space of surfaces
    • M. Bauer, P. Harms and P. W. Michor, Sobolev metrics on shape space of surfaces, J. Geom. Mech. 3(4) (2011), 389-438.
    • (2011) J. Geom. Mech. , vol.3 , Issue.4 , pp. 389-438
    • Bauer, M.1    Harms, P.2    Michor, P.W.3
  • 11
    • 0002299746 scopus 로고    scopus 로고
    • The tangent space in sub-Riemannian geometry
    • (Birkhäuser, Basel)
    • A. Bellaïche, The tangent space in sub-Riemannian geometry, in Sub-Riemannian Geometry, Progress in Mathematics, Volume 144, pp. 1-78 (Birkhäuser, Basel, 1996).
    • (1996) Sub-Riemannian Geometry, Progress in Mathematics , vol.144 , pp. 1-78
    • Bellaïche, A.1
  • 12
    • 84865458344 scopus 로고    scopus 로고
    • Anthropomorphic image reconstruction via hypoelliptic diffusion
    • U. Boscain, J. Duplaix, J. P. Gauthier and F. Rossi, Anthropomorphic image reconstruction via hypoelliptic diffusion, SIAM J. Control Optim. 50(3) (2012), 1309-1336.
    • (2012) SIAM J. Control Optim. , vol.50 , Issue.3 , pp. 1309-1336
    • Boscain, U.1    Duplaix, J.2    Gauthier, J.P.3    Rossi, F.4
  • 13
    • 84902766595 scopus 로고    scopus 로고
    • Hypoelliptic heat kernel over 3-step nilpotent Lie groups
    • U. Boscain, J. P. Gauthier and F. Rossi, Hypoelliptic heat kernel over 3-step nilpotent Lie groups, J. Math. Sci. 199(6) (2014), 614-628.
    • (2014) J. Math. Sci. , vol.199 , Issue.6 , pp. 614-628
    • Boscain, U.1    Gauthier, J.P.2    Rossi, F.3
  • 15
    • 33745442819 scopus 로고    scopus 로고
    • Genericity results for singular curves
    • Y. Chitour, F. Jean and E. Trélat, Genericity results for singular curves, J. Differential Geom. 73(1) (2006), 45-73.
    • (2006) J. Differential Geom. , vol.73 , Issue.1 , pp. 45-73
    • Chitour, Y.1    Jean, F.2    Trélat, E.3
  • 16
    • 55549106807 scopus 로고    scopus 로고
    • Singular trajectories of control-affine systems
    • Y. Chitour, F. Jean and E. Trélat, Singular trajectories of control-affine systems, SIAM J. Control Optim. 47(2) (2008), 1078-1095.
    • (2008) SIAM J. Control Optim. , vol.47 , Issue.2 , pp. 1078-1095
    • Chitour, Y.1    Jean, F.2    Trélat, E.3
  • 17
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • R. J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98(3) (1989), 511-547.
    • (1989) Invent. Math. , vol.98 , Issue.3 , pp. 511-547
    • DiPerna, R.J.1    Lions, P.-L.2
  • 18
    • 34250236182 scopus 로고
    • Controllability criterion for systems in a Banach space (generalization of Chow's theorem)
    • P. I. Dudnikov and S. N. Samborski, Controllability criterion for systems in a Banach space (generalization of Chow's theorem), Ukrain. Mat. Zh. 32(5) (1980), 649-653.
    • (1980) Ukrain. Mat. Zh. , vol.32 , Issue.5 , pp. 649-653
    • Dudnikov, P.I.1    Samborski, S.N.2
  • 19
    • 0032162543 scopus 로고    scopus 로고
    • Variational problems on ows of diffeomorphisms for image matching
    • P. Dupuis, U. Grenander and M. I. Miller, Variational problems on ows of diffeomorphisms for image matching, Quart. Appl. Math. 56(3) (1998), 587-600.
    • (1998) Quart. Appl. Math. , vol.56 , Issue.3 , pp. 587-600
    • Dupuis, P.1    Grenander, U.2    Miller, M.I.3
  • 20
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible uid
    • D. G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible uid, Ann. of Math. (2) 92 (1970), 102-163.
    • (1970) Ann. of Math. , vol.92 , Issue.2 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 22
    • 0042297486 scopus 로고    scopus 로고
    • Form preserving diffeomorphisms on open manifolds
    • J. Eichhorn and R. Schmid, Form preserving diffeomorphisms on open manifolds, Ann. Global Anal. Geom. 14(2) (1996), 147-176.
    • (1996) Ann. Global Anal. Geom. , vol.14 , Issue.2 , pp. 147-176
    • Eichhorn, J.1    Schmid, R.2
  • 23
    • 77952882810 scopus 로고    scopus 로고
    • Mass transportation on sub-Riemannian manifolds
    • A. Figalli and L. Rifford, Mass transportation on sub-Riemannian manifolds, Geom. Funct. Anal. 20(1) (2010), 124-159.
    • (2010) Geom. Funct. Anal. , vol.20 , Issue.1 , pp. 124-159
    • Figalli, A.1    Rifford, L.2
  • 24
    • 0032298437 scopus 로고    scopus 로고
    • Computational anatomy: An emerging discipline
    • Current and future challenges in the applications of mathematics (Providence, RI, 1997)
    • U. Grenander and M. I. Miller, Computational anatomy: an emerging discipline, Quart. Appl. Math. 56(4) (1998), 617-694; Current and future challenges in the applications of mathematics (Providence, RI, 1997).
    • (1998) Quart. Appl. Math. , vol.56 , Issue.4 , pp. 617-694
    • Grenander, U.1    Miller, M.I.2
  • 25
    • 85026480367 scopus 로고    scopus 로고
    • Sub-riemannian geometry on infinitedimensional manifolds
    • (to appear), arXiv:1201.2251
    • E. Grong, I. Markina and A. Vasil'ev, Sub-riemannian geometry on infinitedimensional manifolds, J. Geom. Anal. (2012) (to appear), arXiv:1201.2251.
    • (2012) J. Geom. Anal.
    • Grong, E.1    Markina, I.2    Vasil'Ev, A.3
  • 26
    • 0033241656 scopus 로고    scopus 로고
    • Homogeneity of infinite dimensional isoparametric submanifolds
    • (2)
    • E. Heintze and X. Liu, Homogeneity of infinite dimensional isoparametric submanifolds, Ann. of Math. (2) 149(1) (1999), 149-181.
    • (1999) Ann. of Math. , vol.149 , Issue.1 , pp. 149-181
    • Heintze, E.1    Liu, X.2
  • 27
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • 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), 1-81.
    • (1998) Adv. Math. , vol.137 , pp. 1-81
    • Holm, D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 28
    • 72749090185 scopus 로고    scopus 로고
    • A nonholonomic Moser theorem and optimal transport
    • B. Khesin and P. Lee, A nonholonomic Moser theorem and optimal transport, J. Symplectic Geom. 7(4) (2009), 381-414.
    • (2009) J. Symplectic Geom. , vol.7 , Issue.4 , pp. 381-414
    • Khesin, B.1    Lee, P.2
  • 30
    • 0017001951 scopus 로고
    • On the existence and nonexistence of Lagrange multipliers in Banach spaces
    • S. Kurcyusz., On the existence and nonexistence of Lagrange multipliers in Banach spaces, J. Optim. Theory Appl. 20(1) (1976), 81-110.
    • (1976) J. Optim. Theory Appl. , vol.20 , Issue.1 , pp. 81-110
    • Kurcyusz, S.1
  • 31
    • 0037490329 scopus 로고
    • Optimal control theory for infinite-dimensional systems
    • (Birkhäuser Boston Inc., Boston, MA)
    • X. J. Li and J. M. Yong, Optimal control theory for infinite-dimensional systems, in Systems & Control: Foundations & Applications (Birkhäuser Boston Inc., Boston, MA, 1995).
    • (1995) Systems & Control: Foundations & Applications
    • Li, X.J.1    Yong, J.M.2
  • 32
    • 0003274786 scopus 로고    scopus 로고
    • Introduction to mechanics and symmetry
    • xviii+582 2nd ed., Texts in Applied Mathematics, (Springer-Verlag, New York)
    • J. E. Marsden and T. S. Ratiu, Introduction to mechanics and symmetry, in A Basic Exposition of Classical Mechanical Systems, 2nd ed., Texts in Applied Mathematics, Volume 17 (Springer-Verlag, New York, 1999). xviii+582 pp.
    • (1999) A Basic Exposition of Classical Mechanical Systems , vol.17
    • Marsden, J.E.1    Ratiu, T.S.2
  • 33
    • 34249788990 scopus 로고    scopus 로고
    • An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
    • 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(1) (2007), 74-113.
    • (2007) Appl. Comput. Harmon. Anal. , vol.23 , Issue.1 , pp. 74-113
    • Michor, P.W.1    Mumford, D.2
  • 35
    • 84968494100 scopus 로고
    • On the volume elements on a manifold
    • J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294.
    • (1965) Trans. Amer. Math. Soc. , vol.120 , pp. 286-294
    • Moser, J.1
  • 38
    • 17444430784 scopus 로고    scopus 로고
    • Morse-Sard type results in sub-Riemannian geometry
    • L. Rifford and E. Trélat, Morse-Sard type results in sub-Riemannian geometry, Math. Ann. 332(1) (2005), 145-159.
    • (2005) Math. Ann. , vol.332 , Issue.1 , pp. 145-159
    • Rifford, L.1    Trélat, E.2
  • 39
    • 84911950740 scopus 로고    scopus 로고
    • Controllability on infinite-dimensional manifolds: A Chow-Rashevsky theorem
    • M. K. Salehani and I. Markina, Controllability on infinite-dimensional manifolds: a Chow-Rashevsky theorem, Acta Appl. Math. 134(1) (2014), 229-246.
    • (2014) Acta Appl. Math. , vol.134 , Issue.1 , pp. 229-246
    • Salehani, M.K.1    Markina, I.2
  • 40
    • 33749020978 scopus 로고    scopus 로고
    • Infinite dimensional Lie groups with applications to mathematical physics
    • R. Schmid, Infinite dimensional Lie groups with applications to mathematical physics, J. Geom. Symmetry Phys. 1 (2004), 54-120.
    • (2004) J. Geom. Symmetry Phys. , vol.1 , pp. 54-120
    • Schmid, R.1
  • 42
    • 0000943845 scopus 로고
    • Action de groupe de dimension infinie et reconnaissance de formes
    • A. Trouvé, Action de groupe de dimension infinie et reconnaissance de formes, C. R. Acad. Sci. Paris I 321(8) (1995), 1031-1034.
    • (1995) C. R. Acad. Sci. Paris I , vol.321 , Issue.8 , pp. 1031-1034
    • Trouvé, A.1
  • 43
    • 84930086876 scopus 로고    scopus 로고
    • Diffeomorphism groups and pattern matching in image analysis
    • A. Trouvé, Diffeomorphism groups and pattern matching in image analysis, Int. J. Comput. Vis. 37(1) (2005), 17.
    • (2005) Int. J. Comput. Vis. , vol.37 , Issue.1 , pp. 17
    • Trouvé, A.1
  • 44
    • 33144468544 scopus 로고    scopus 로고
    • Local geometry of deformable templates
    • (electronic)
    • A. Trouvé and L. Younes, Local geometry of deformable templates, SIAM J. Math. Anal. 37(1) (2005), 17-59 (electronic).
    • (2005) SIAM J. Math. Anal. , vol.37 , Issue.1 , pp. 17-59
    • Trouvé, A.1    Younes, L.2


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