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Volumn 23, Issue 1, 2013, Pages 334-366

Geometry of Diffeomorphism Groups, Complete integrability and Geometric statistics

Author keywords

curvature; Diffeomorphism groups; Euler Arnold equations; Fisher Rao metric; geodesics; Hellinger distance; integrable systems; Riemannian metrics

Indexed keywords


EID: 84875665207     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-013-0210-2     Document Type: Article
Times cited : (81)

References (29)
  • 4
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou J.-D., Brenier Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numerical Mathematics 84, 375-393 (2001).
    • (2001) Numerical Mathematics , vol.84 , pp. 375-393
    • Benamou, J.-.D.1    Brenier, Y.2
  • 5
    • 84875662992 scopus 로고    scopus 로고
    • Integrable geodesic flow on homogeneous spaces
    • Appendix C by A. V. Borisov, I. S. Mamaev, Izhevsk and personal communication (2010)
    • A. Bolsinov, Integrable geodesic flow on homogeneous spaces, Appendix C. In: Modern Methods in the Theory of Integrable Systems by A. V. Borisov, I. S. Mamaev, Izhevsk, 2003, 236-254, and personal communication (2010).
    • (2003) Modern Methods in the Theory of Integrable Systems , pp. 236-254
    • Bolsinov, A.1
  • 6
    • 0009226254 scopus 로고
    • Statistical Decision Rules and Optimal Inference
    • Providence
    • N. N. Chentsov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Providence (1982).
    • (1982) American Mathematical Society
    • Chentsov, N.N.1
  • 8
    • 0001700430 scopus 로고
    • Further comments on some comments on a paper by Bradley Efron
    • Dawid A. P.: Further comments on some comments on a paper by Bradley Efron. Annals of Statistics 5(6), 1249 (1977).
    • (1977) Annals of Statistics , vol.5 , Issue.6 , pp. 1249
    • Dawid, A.P.1
  • 9
    • 0002984718 scopus 로고
    • The manifold of Riemannian metrics
    • American Mathematical Society, Providence
    • D. Ebin, The manifold of Riemannian metrics, In: Proceedings of Symposia in Pure Mathematics 15, American Mathematical Society, Providence, (1970).
    • (1970) Proceedings of Symposia in Pure Mathematics 15
    • Ebin, D.1
  • 10
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • Ebin D., Marsden J. E.: Groups of diffeomorphisms and the motion of an incompressible fluid. Annals of Mathematics 92, 102-163 (1970).
    • (1970) Annals of Mathematics , vol.92 , pp. 102-163
    • Ebin, D.1    Marsden, J.E.2
  • 11
    • 0000551847 scopus 로고
    • Defining the curvature of a statistical problem (with applications to second order efficiency)
    • Efron B.: Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics 3(6), 1189-1242 (1975).
    • (1975) Annals of Statistics , vol.3 , Issue.6 , pp. 1189-1242
    • Efron, B.1
  • 12
    • 0000339711 scopus 로고
    • The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group
    • Freed D. S., Groisser D.: The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group. Michigan Mathematics Journal 36, 323-344 (1989).
    • (1989) Michigan Mathematics Journal , vol.36 , pp. 323-344
    • Freed, D.S.1    Groisser, D.2
  • 14
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • Holm D., Marsden J. E., Ratiu T. S.: The Euler-Poincaré equations and semidirect products with applications to continuum theories. Advances in Mathematics 137, 1-81 (1998).
    • (1998) Advances in Mathematics , vol.137 , pp. 1-81
    • Holm, D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 16
    • 0037612018 scopus 로고    scopus 로고
    • Euler equations on homogeneous spaces and Virasoro orbits
    • Khesin B., Misiołek G.: Euler equations on homogeneous spaces and Virasoro orbits. Advances in Mathematics 176, 116-144 (2003).
    • (2003) Advances in Mathematics , vol.176 , pp. 116-144
    • Khesin, B.1    Misiołek, G.2
  • 19
    • 34547608701 scopus 로고    scopus 로고
    • The Hunter-Saxton equation describes the geodesic flow on a sphere
    • Lenells J.: The Hunter-Saxton equation describes the geodesic flow on a sphere. Journal of Geometry and Physics 57, 2049-2064 (2007).
    • (2007) Journal of Geometry and Physics , vol.57 , pp. 2049-2064
    • Lenells, J.1
  • 20
    • 35248813847 scopus 로고    scopus 로고
    • Weak geodesic flow and global solutions of the Hunter-Saxton equation
    • Lenells J.: Weak geodesic flow and global solutions of the Hunter-Saxton equation. Discrete and Continuous Dynamical Systems 18(4), 643-656 (2007).
    • (2007) Discrete and Continuous Dynamical Systems , vol.18 , Issue.4 , pp. 643-656
    • Lenells, J.1
  • 21
    • 77951203607 scopus 로고    scopus 로고
    • Fredholm properties of Riemannian exponential maps on diffeomorphism groups
    • Misiołek G., Preston S. C.: Fredholm properties of Riemannian exponential maps on diffeomorphism groups. Inventiones Mathematicae 179(1), 191-227 (2010).
    • (2010) Inventiones Mathematicae , vol.179 , Issue.1 , pp. 191-227
    • Misiołek, G.1    Preston, S.C.2
  • 23
    • 61349157348 scopus 로고    scopus 로고
    • Well-posedness of the generalized Proudman-Johnson equation
    • Okamoto H.: Well-posedness of the generalized Proudman-Johnson equation. Journal of Mathematical Fluid Mechanics 11(1), 46-59 (2009).
    • (2009) Journal of Mathematical Fluid Mechanics , vol.11 , Issue.1 , pp. 46-59
    • Okamoto, H.1
  • 24
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: the porous medium equation
    • Otto F.: The geometry of dissipative evolution equations: the porous medium equation. Communications in Partial Differential Equations 26, 101-174 (2001).
    • (2001) Communications in Partial Differential Equations , vol.26 , pp. 101-174
    • Otto, F.1
  • 25


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.