메뉴 건너뛰기




Volumn 43, Issue 4, 2013, Pages 385-395

The energy functional on the Virasoro-Bott group with the L2-metric has no local minima

Author keywords

Diffeomorphism group; Geodesic distance; Virasoro group

Indexed keywords


EID: 84876014024     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10455-012-9350-0     Document Type: Article
Times cited : (2)

References (14)
  • 1
    • 0001356905 scopus 로고
    • Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • Arnold V. I.: Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16, 319-361 (1966).
    • (1966) Ann. Inst. Fourier , vol.16 , pp. 319-361
    • Arnold, V.I.1
  • 2
    • 84857458962 scopus 로고    scopus 로고
    • Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
    • Bauer M., Bruveris M., Harms P., Michor P.: Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation. Ann. Global Anal. Geom. 41, 461-472 (2012).
    • (2012) Ann. Global Anal. Geom. , vol.41 , pp. 461-472
    • Bauer, M.1    Bruveris, M.2    Harms, P.3    Michor, P.4
  • 4
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • Constantin A., Kolev B.: Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78(4), 787-804 (2003).
    • (2003) Comment. Math. Helv. , vol.78 , Issue.4 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 5
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • Ebin D. G., Marsden J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math. (2) 92, 102-163 (1970).
    • (1970) Ann. Math. (2) , vol.92 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 6
    • 84866317052 scopus 로고    scopus 로고
    • Well-posedness of higher dimensional Camassa-Holm equations
    • Gay-Balmaz F.: Well-posedness of higher dimensional Camassa-Holm equations. Bull. Transilv. Univ. Braşov Ser. III 2(51), 55-58 (2009).
    • (2009) Bull. Transilv. Univ. Braşov Ser. III , vol.2 , Issue.51 , pp. 55-58
    • Gay-Balmaz, F.1
  • 9
    • 85045532817 scopus 로고    scopus 로고
    • Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach
    • In: Bove, A., Colombini, F., Del Santo, D. (eds.) of Progress in Nonlinear Differential Equations and their Applications Birkhäuser, Boston
    • Michor, P. W.: Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach. In: Bove, A., Colombini, F., Del Santo, D. (eds.) Phase Space Analysis of Partial Differential Equations, volume 69 of Progress in Nonlinear Differential Equations and their Applications, pp. 133-215. Birkhäuser, Boston (2006).
    • (2006) Phase Space Analysis of Partial Differential Equations , vol.69 , pp. 133-215
    • Michor, P.W.1
  • 10
    • 29244431608 scopus 로고    scopus 로고
    • Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
    • (electronic)
    • Michor, P. W., Mumford, D.: Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Doc. Math. 10, 217-245 (electronic) (2005).
    • (2005) Doc. Math. , vol.10 , pp. 217-245
    • Michor, P.W.1    Mumford, D.2
  • 11
    • 22444453467 scopus 로고    scopus 로고
    • Geometry of the Virasoro-Bott group
    • Michor P. W., Ratiu T.: Geometry of the Virasoro-Bott group. J. Lie Theory 8, 293-309 (1998).
    • (1998) J. Lie Theory , vol.8 , pp. 293-309
    • Michor, P.W.1    Ratiu, T.2
  • 12
    • 0039072121 scopus 로고    scopus 로고
    • Conjugate points in the Bott-Virasoro group and the KdV equation
    • Misiołek G.: Conjugate points in the Bott-Virasoro group and the KdV equation. Proc. Amer. Math. Soc. 125(3), 935-940 (1997).
    • (1997) Proc. Amer. Math. Soc. , vol.125 , Issue.3 , pp. 935-940
    • Misiołek, G.1
  • 13
    • 34250093431 scopus 로고
    • Korteweg-de Vries superequations as an Euler equation
    • Ovsienko V. Y., Khesin B. A.: Korteweg-de Vries superequations as an Euler equation. Funct. Anal. Appl. 21, 329-331 (1987).
    • (1987) Funct. Anal. Appl. , vol.21 , pp. 329-331
    • Ovsienko, V.Y.1    Khesin, B.A.2
  • 14
    • 0001120168 scopus 로고
    • The geometry of the KdV equation. Topological methods in quantum field theory (Trieste, 1990)
    • Segal G.: The geometry of the KdV equation. Topological methods in quantum field theory (Trieste, 1990). Internat. J. Modern Phys. A 6(16), 2859-2869 (1991).
    • (1991) Internat. J. Modern Phys. A , vol.6 , Issue.16 , pp. 2859-2869
    • Segal, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.